Trigonometry

 

Trigonometry Videos

 

Chapters and section order are based on Trigonometry, 9th Edition, Lial, Hornsby, Schneider, Addison-Wesley

 

Ch 1  Trigonometric Functions

 

Ch 1.1  Angles

Angle Basics – Ray, Positive Angle, Negative Angle, Degree, Acute, Obtuse, Right, Straight, and Reflex angle, Complementary Angle, Supplementary Angle
http://www.youtube.com/watch?v=7iBc5bJdanI

 

Animation: Types of Angles – Acute, Obtuse, Right, Straight, and Reflex angle
http://www.youtube.com/watch?v=50eVno0s1DI&feature=relmfu

 

Adjacent, Complementary, Supplementary, and Vertical Angles
http://www.youtube.com/watch?v=rjOjwcV79HM&feature=relmfu

 

Degrees, Minutes, and Seconds
http://www.youtube.com/watch?v=tQLB1riYtz4&feature=relmfu

 

Animation: Angles in Standard Position
http://www.youtube.com/watch?v=hpIjaKLOo6o&feature=relmfu

 

Finding the Quadrant in Which an Angle Lies :

Examples :45º, 195º, -20º, –72º, 340º, 120º
http://www.youtube.com/watch?v=GIMMX55C9iU&feature=relmfu

Examples :380º, 1240º, –445º
http://www.youtube.com/watch?v=dfd8IlsXZgk&feature=relmfu

Examples :25º, –255º, –580º
http://www.youtube.com/watch?v=E0vPI3PPBBk&feature=relmfu

 

Angles in Standard Position Quadrantal Angle, and Coterminal Angles :

Coterminal Angles of 135º, 1070º, –65º, 90º
http://www.youtube.com/watch?v=Xtk1PVRoDLQ&feature=relmfu

Coterminal Angles of 45º, 135º, –255º, 90º
http://www.youtube.com/watch?v=dz5YpNFuhRQ&feature=relmfu

Determining if the pairs of angles are Coterminal Angles
http://www.youtube.com/watch?v=VV3rSBae-KY&feature=relmfu 

Determining Positive and Negative Coterminal Angle of 68º
http://www.youtube.com/watch?v=m7jTGVVzb0s&feature=relmfu

 


 

Ch 1.2   Angle Relationships and Similar Triangles

Angle Relationships and Types of Triangles – Vertical Angle, Interior Angles, Equilateral Triangle, Isosceles Triangle, Scalene Triangle, Right Triangle, Acute Triangle, Obtuse Triangle, Sum of Measures of Angles
http://www.youtube.com/watch?v=z_O2Knid2XA

 

Similar Polygons – Properties of Similar Polygons, Solve the Similar Triangles
http://www.youtube.com/watch?v=AFEDUm4bPHk

 

Congruent and Similar Triangles – Conditions for Similar Triangles, Solve for Similar Triangles
http://www.youtube.com/watch?v=OEp7YK6WEXE&feature=relmfu

 

Sum of Interior Angles in a Triangle
http://www.youtube.com/watch?v=GQERWzwaYcg

 

 

 

 

Ch 1.3  Trigonometric Functions

Introduction to Six Trigonometric Functions Using Triangles – Sine, Cosine, Tangent, Secant, Cosecant, Cotangent
http://www.youtube.com/watch?v=Ujyl_zQw2zE

 

Introduction to Six Trigonometric Functions Using Angles (in a Unit Circle) – Sine, Cosine, Tangent, Secant, Cosecant, Cotangent
http://www.youtube.com/watch?v=vaG4O6d48mo&feature=relmfu

Six Trigonometric Functions of Quadrantal Angles (0º, 90º, 180º, 270º)
http://www.youtube.com/watch?v=k9ih_86XkOQ

Finding The Trigonometric Function value based on a Coordinate :

Finding the Trigonometric Function values of Cotangent and Tangent with Coordinate of (3, 4)
http://www.youtube.com/watch?v=Y6moR4ksAZA&feature=relmfu

Finding the Trigonometric Function value of Secant with Coordinate of (5, 6)
http://www.youtube.com/watch?v=Z53Tf5gMrgg&list=PL86281C72D802CE05&index=25&feature=plpp_video

Finding the Trigonometric Function values of Sine and Cosine with coordinate of (7, –2)
http://www.youtube.com/watch?v=sM8CTuG349I&list=PL86281C72D802CE05&index=26&feature=plpp_video

Finding the Six Trigonometric Function Values with Coordinate of (10, –6)
http://www.youtube.com/watch?v=hCckoLUDIAc


 

Ch 1.4  Using the Definitions of the Trigonometric Functions

Finding Trigonometric Function Values Given One Trig Value in a Right Triangle
cosθ=
http://www.youtube.com/watch?v=GWdQ9nfyN3Y&feature=relmfu

Finding the Area of the Triangle
http://www.youtube.com/watch?v=AK3GgzWSHJc&feature=relmfu

Finding the Missing Length and Cotangent Value
http://www.youtube.com/watch?v=7hDW_snc62I&feature=relmfu

Fundamental Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities, and use identities to solve for angles :

Determining sec θ Given cos θ=
Determining cot θ Given tan θ=5
Determining cos θ Given sec θ=
Finding sin θ and tan θ Given that cos θ=  and sin θ>0
Finding sin θ and cos θ Given that tan θ=  and θ is in Quadrant III
http://www.youtube.com/watch?v=4BR_qUZ5jK0&feature=relmfu

Finding sin θ and tan θ Given that cos θ=  and θ is in Quadrant IV
Finding sec θ and sin θ Given that cos θ=  and θ is in Quadrant II
Finding Six Exact Trigonometric Function Values Given the Point (–2, –4) on the Terminal Side of θ
http://www.youtube.com/watch?v=OmJ5fxyXrfg

Determining the Quadrant of the Terminal Side of an Angle Given Trig Function Signs
http://www.youtube.com/watch?v=wlE1XM97EJc


 

Finding Trigonometric Values Given One Trigonometric Value :

Finding sec θ, csc θ, tan θ and cot θ from sin θ=  and cos θ=
http://www.youtube.com/watch?v=iQlZIlrQ-3s&list=PL86281C72D802CE05&index=31&feature=plpp_video

Finding cos θ from tan θ=  and cos θ<0
http://www.youtube.com/watch?v=kgiTSGr6obs&list=PL86281C72D802CE05&index=32&feature=plpp_video

Finding the Five Remaining Trigonometric Function Values from cos θ=  and θ is in Quadrant IV
http://www.youtube.com/watch?v=wY25sbabTPk

 

 

 

Ch 2  Acute Angles and Right Triangles

 

Ch 2.1  Trigonometric Functions of Acute Angles

 

Cofunction Identities
http://www.youtube.com/watch?v=_gkuml–4_Q&feature=youtu.be

30–60–90 and 45–45–90 Triangles and the Relationship of the Sides of the Right Triangles :

sin 30º,cos 30º, tan 30, sin 60º,cos 60º, tan 60º, sin 45º,cos 45º, tan 45º
http://www.youtube.com/watch?v=6Cb-XzSMXo4

Using the Ratio of the Sides of 30–60–90 Triangle or 45-45-90 Triangle to solve the Triangles
http://www.youtube.com/watch?v=b6MsSkXYQo4

Examples: Solve a 30–60–90 Right Triangle
http://www.youtube.com/watch?v=qOZeOCwwUkE

Examples: Solve a 45–45–90  Right Triangle
http://www.youtube.com/watch?v=Ucy2mUCcMIs

 

 

Ch 2.2  Trigonometric Functions of Non-Acute Angles

Examples: Determine the Reference Angle for a Given Angle :

θ=221º, θ=347º, θ= –125º
http://www.youtube.com/watch?v=YJNSRvhd3uA

cos 210º, tan (–45)º
http://www.youtube.com/watch?v=eh_rN2N-niE&list=PL86281C72D802CE05&index=29&feature=plpp_video

θ=460º, θ=165º, θ= –40º, θ= –283º
http://www.youtube.com/watch?feature=player_embedded&v=qgGFQXnuszk

Determining Trigonometric Function Values Using Reference Angles and Reference Triangles :

Reference Angles of 120º, 210º, –45º, 270º
http://www.youtube.com/watch?v=D6RP_ttfT4M

Trigonometric Function of sin (–150º), cos 960º, tan 180º, csc 225º, sec (–240º), cot 540º from a Unit Circle
http://www.youtube.com/watch?v=i56P6xzsB5Y

Trigonometric Function Values of 90º, 150º, –60º, from a unit Circle
http://www.youtube.com/watch?v=wGFOlLJz24I

Trigonometric Function Values of –990º from a unit Circle
http://www.youtube.com/watch?v=BFtqhHgXSMk

 

 

 

Ch 2.3  Finding Trigonometric Function Values Using a Calculator

Determining Trigonometric Function Values on the Calculator :
sin 30º, cos 45º, tan (–264º), sec (102.5º), csc (432º), cot (–23.45º)
http://www.youtube.com/watch?v=rhRi_IuE_18

 

Using Inverse Trigonometric functions to Find Angles :

Solving for θ for sin θ=0.7523, tan θ=3.54, and Find the Sides and Angles of a Right Triangle
http://www.youtube.com/watch?v=JutzksM5PN4

Solving for θ for cos-1( ) and tan-1(–1)
http://www.youtube.com/watch?v=nPeDoGwtPNc

Finding the Trigonometric Function Values Using Calculator: cos 369.18°, tan 426.62°, sin 46.6°, cot 17.9°
Solving for θ for csc θ=3.6, cot θ=2.1, csc θ=1.63, sec θ=7.25
http://www.youtube.com/watch?v=M7z2n1KpIEg


 

Ch 2.4  Solving Right Triangles

Example: Determining the Measure of an Angle of a Right Triangle Using a Trig Equation
http://www.youtube.com/watch?v=ypgcPKH4m4A

Solving the sides and angles of Right Triangles
http://www.youtube.com/watch?v=p6hcLw4lzTQ

Applications : Angle of Elevation
http://www.youtube.com/watch?v=-QOEcnuGQwo

Finding the Height of an Object

Finding the Height of a Tree
http://www.youtube.com/watch?v=-2w7Mdq5C58

Finding the Height of a Flagpole (Part 1 of the video)
http://www.youtube.com/watch?v=-QOEcnuGQwo

 

Simple Distance Problem – A Hiking Problem
http://www.youtube.com/watch?v=ErVTgggAQjs&list=PL86281C72D802CE05&index=49&feature=plpp_video

Determining the Speed of a Boat
http://www.youtube.com/watch?v=LXPu-POyb4s&list=PL86281C72D802CE05&index=50&feature=plpp_video


 

Ch 2.5  Further Applications of Right Triangles

Applications : Finding the Distance of a Ship on an Angle of Bearing (Part 2 of the video)
http://www.youtube.com/watch?v=-QOEcnuGQwo

Finding the Height of a Building
http://www.youtube.com/watch?v=y0b90Yz-LPM&list=PL86281C72D802CE05&index=48&feature=plpp_video

Finding the Length of x Using Right Triangle Trigonometry
http://www.youtube.com/watch?v=j0uwY8zpMeg
http://www.youtube.com/watch?v=gfgtkeN5m8k
http://www.youtube.com/watch?v=Vf0LnQOaSxM


 

Ch 3  Radian Measure and Circular Functions

Ch 3.1  Radian Measure

 

Showing the Relationship between Degree and Radian, and Converting Angles from Degree 120º to Radian
http://www.youtube.com/watch?v=cLBKOYmHuDM&list=PL86281C72D802CE05&index=22&feature=plpp_video

 

Angle Measured in Radian, Converting Angles from Degrees to Radians, and from Radians to Degrees
http://www.youtube.com/watch?v=nAJqXtzwpXQ

Examples: Converting Angles 135º. –60º, 15º, 48º to Radian
http://www.youtube.com/watch?v=25NuDwXAja0

Examples: Converting Angles of , , and 2.1 in Radian to Degree
http://www.youtube.com/watch?v=I-36SsQ9KgQ

Examples: Determining Coterminal Angles of  and
http://www.youtube.com/watch?v=tpr8FkiowHk

Examples: Determine Six Trig Function Values of  Using Reference Triangles
http://www.youtube.com/watch?v=t5DEezFe07U


 

Ch 3.2  Applications of Radian Measure

Arc Length and Area of a Sector :

Finding Arc Length from r=9.5, θ=120º
Finding the Difference of Arc Length of d=12ft and d=11.81ft
Finding Area of a Sector from r=450, θ=240º
http://www.youtube.com/watch?v=zD4CsKIYEHo

Finding Arc Length from r=3cm, θ=120º
Finding the Distance of Earth’s Path Around the Sun in One Month from  r=93 Million Miles
http://www.youtube.com/watch?v=qp0cATM2yys

Examples: Area of a Sector and Area Bounded by a Chord and Arc
Finding Area of a Sector from r=8, θ=110º
Finding Area of a Sector from r=12, θ=80º
http://www.youtube.com/watch?v=c2avS8NLspU


 

Ch 3.3  The Unit circle and Circular Functions

A way to remember the Entire Unit Circle for Trigonometry
http://www.youtube.com/watch?feature=player_embedded&v=cIVpemcoAlY

Tricks to remember Trigonometry values in First Quadrant  http://www.youtube.com/watch?feature=player_embedded&v=ao4EJzNWmK8

Tricks to remember Angles in Radians
http://www.youtube.com/watch?v=Q4KbPrK4DlE


 

Ch 3.4  Linear and Angular Speed

Linear Velocity and Angular Velocity
http://www.youtube.com/watch?v=jh9gRYAuau8

Example: Determine the Number of Revolutions Per Second of a Car Tire
http://www.youtube.com/watch?v=3EBhZA0QZWg

Example: Determine Angular and Linear Velocity of Two Particles Running in Concentric Circles
http://www.youtube.com/watch?v=bfWkgA5GSE0


 

Ch 4  Graphs of the Circular Functions

Ch 4.1  Graphs of the Sine and Cosine Functions

Graphing the Sine and Cosine Function
http://www.youtube.com/watch?v=nXx2PsgMjYA

Graphing Sine and Cosine with Different Coefficients (Amplitude and Period) :

Finding the Period of y=cos(3x), and y=sin( )
Finding and Graphing the Amplitude and Period of  y=sin( ), y= cos(2x) and y= –2sin(3x)
http://www.youtube.com/watch?v=qJ-oUV7xL3w

Finding the Amplitude and Period of y= –4cos(3x), y= sin(x) and y= cos( x)
http://www.youtube.com/watch?v=kiuV-DAlopE&list=PL86281C72D802CE05&index=36&feature=plpp_video

Describing the Transformation of y= –3cos(6x)
http://www.youtube.com/watch?v=e2OvNpG218Y

Graphing y = –2 cos(2x)
http://www.youtube.com/watch?feature=player_embedded&v=vnGE716t9Yk


 

Ch 4.2  Translations of the Graphs of the Sine and Cosine Functions

Graphing Sine and Cosine with Phase Shifts (Horizontal Translation), Example 1 and Example 2 :

Phase Shifts (Horizontal Translation) for y=cos(x–4), y=sin[2(x+1)], and y=cos(10x+30)
http://www.youtube.com/watch?feature=player_embedded&v=zjSgkoaL_5A

Which Graph Most Closely Resembles the Graph of y= –2sin(x–π)
http://www.youtube.com/watch?feature=player_embedded&v=RzZyyIu9IvA

Horizontal and Vertical Translations of Sine Cosine :

Vertical Translation of y=sin (x)+1 and y=cos(x)–
Horizontal and Vertical Translation and Graphing of y=sin(x– )+1, and y= – +cos(x+ )
http://www.youtube.com/watch?v=DswBtrtvR5M

 

Horizontal and Vertical Translation and Graphing of y= +sin(x+ )
http://www.youtube.com/watch?v=Gu0vV73V-no

Graphing Sine and Cosine with Different Coefficients (Amplitude, period, and Vertical Translation) : y=2sin( )–1
http://www.youtube.com/watch?v=klCCKv6bIIg

Graphing Sine and Cosine with Different Coefficients (Amplitude, period, Horizontal Translation, and Vertical Translation) :

y=4cos(4x–8)–1
http://www.youtube.com/watch?v=JI6_7SVtk6E

y=2sin(2 (x+ ))–1
y= cos( x– )+2
y=4–sin (π(x+1)
http://www.youtube.com/watch?v=wUzARNIkH-g

y=2cos (x– )+1
http://www.youtube.com/watch?feature=player_embedded&v=ijTIr-aykUk

 

 

Example: Describe the Transformations of Cosine Function from a Graph : Fill Out Amplitude, Period, Horizontal Transformation (Phase Shift), Vertical Transformation (Vertical Shift), Midline

http://www.youtube.com/watch?v=UkHGsQTV2Qk

http://www.youtube.com/watch?v=Vp6uOaOxUS0

http://www.youtube.com/watch?v=mkU8ZYNfp74

 

 

 

 


 

Ch 4.3  Graphs of the Tangent of Cotangent Functions

Graphing the Tangent Function y=tan θ
http://www.youtube.com/watch?v=6pc95eHUJhY

Example: Graphing the Tangent Function y=tan θ
Using the Unit Circle and the Reciprocal Identity
http://www.youtube.com/watch?v=vCrAYNxbRLM

Graphing the Cotangent Function y=cot θ
http://www.youtube.com/watch?v=5_65h_i8Yxg

Graphing Tangent and over a Different Period y=tan(4x)
http://www.youtube.com/watch?v=CNL4O1ZFvDI

Graphing Tangent and Cotangent over Different Periods and Amplitude :

y=tan(3x)
y=cot( )
y=2tan( )
y= cot(2x)
http://www.youtube.com/watch?v=6bSODTkQ9Mg

y=cot(πx)
y=2cot(πx)
http://www.youtube.com/watch?feature=player_embedded&v=RdJjja1EHbk

Example: Graphing a Transformation of the Cotangent Function y=2cot( x)
http://www.youtube.com/watch?v=-pi-9h8Oh5k

Identifying a Trigonometric a Function from Its Graph
http://www.youtube.com/watch?feature=player_embedded&v=Nu6QUnlH79U

Ch 4.4  Graphs of the Secant and Cosecant Functions

Graphing y=csc θ Using y=sin θ
Graphing y=sec θ Using y=cos θ
http://www.youtube.com/watch?v=5kOgBAVnrCI

Graphing y= –csc θ Using y=sin θ
http://www.youtube.com/watch?feature=player_embedded&v=LupVZLhNDPI

 

 

Example: Graphing a Transformation of Cosecant Function
y=2csc(2πx+π)+3
http://www.youtube.com/watch?v=YbagcqcjBuk

Example: Determine the Domain of the Secant and Cosecant Functions Using the Unit Circle
http://www.youtube.com/watch?v=cwrfDKzQUCI

 

Identifying a Trigonometric a Function from Its Graph
http://www.youtube.com/watch?feature=player_embedded&v=SyREv9mRkyM


 

Ch 5  Trigonometric Identities

Ch 5.1  Trigonometric Identities

Fundamental Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities
http://www.youtube.com/watch?v=OmJ5fxyXrfg

Example: Verifying Pythagorean Identities for a Specific Angle :
Verifying sin2θ+cos2θ=1 for 150º
Verifying tan2θ+1=sec2θ for 45º
http://www.youtube.com/watch?v=KSmaRyDsNDs

Negative Angle identities : sin(–θ), cos(–θ), tan(–θ), csc(–θ), sec(–θ), and cot(–θ)
http://www.youtube.com/watch?v=WEOCLWiDF8Q

Simplifying Trigonometric Expressions Using Identities :

tan3(x)·sec3(x)
http://www.youtube.com/watch?feature=player_embedded&v=SZu_EVV4jjY

sec(x)·cos(x)–cos2(x)
http://www.youtube.com/watch?feature=player_embedded&v=FS6iQX7jY-s

(csc2(x)–1)(sec2(x)·sin2(x))
http://www.youtube.com/watch?feature=player_embedded&v=fkrLkvQSlmk

cotx·tanx–cos2http://www.youtube.com/watch?v=IaSzgJnc5wg&list=PL86281C72D802CE05&index=67&feature=plpp_video

sin2(x)·cos(x)·csc(x)

http://www.youtube.com/watch?v=Hf0AciRDDaE

(1–cos2(x))(1+cot2(x))
http://www.youtube.com/watch?v=C1nJIaxkWPs

Simplifying Trigonometric Expressions Involving Fractions

http://www.youtube.com/watch?feature=player_embedded&v=HGIHD7zee0Q

 
http://www.youtube.com/watch?v=Jx6zJUbWJKY&list=PL86281C72D802CE05&index=55&feature=plpp_video
http://www.youtube.com/watch?v=3cZDPvJ7wMs
http://www.youtube.com/watch?v=yRFzinqxt9o
http://www.youtube.com/watch?v=VLBUtX5tuJE


 

Ch 5.2  Verifying Trigonometric Identities

Simplifying Products of Binomials Involving Trigonometric Functions :

(cos(x)–1)(cos(x)+1)
(sec(x)+tan(x))(sec(x)–tan(x))
http://www.youtube.com/watch?v=e0K-gWF9Y5g&list=PL86281C72D802CE05&index=56&feature=plpp_video

[tan(θ)+cos2(θ)+sin2(θ)][tan(θ)–cos2(θ)–sin2(θ)]
http://www.youtube.com/watch?v=jbxM8CSOOLg&list=PL86281C72D802CE05&index=57&feature=plpp_video

Factoring Trigonometric Expressions :

sin2(θ)+cot2(θ) sin2(θ)

http://www.youtube.com/watch?v=2tiv14iok0k&list=PL86281C72D802CE05&index=58&feature=plpp_video

2cos2(x)+2cos (x)–24  http://www.youtube.com/watch?v=IHieGivL8Cw&list=PL86281C72D802CE05&index=59&feature=plpp_video

 

Verifying that each Trigonometric Equation is An Identity :

cos(θ)tan(θ)=sin(θ);
;
;
; sin4(θ)–cos4(θ)=2sin2(θ)–1
http://www.youtube.com/watch?v=Zktxkfr9zJE

tan(x)+cot (x)=sec(x)csc(x);
;

http://www.youtube.com/watch?v=zJTpoogPoJk

cos(θ)tan(θ)=sin(θ);
cos(x)[csc(x)tan(x)]=cot(x)+sin(x);
;
http://www.youtube.com/watch?v=9uoKutwuCio

 
http://www.youtube.com/watch?feature=player_embedded&v=IE8q4WRubC4

http://www.youtube.com/watch?v=4QmzqwQSt8A&list=PL86281C72D802CE05&index=65&feature=plpp_video

http://www.youtube.com/watch?v=dpFhEqdS3bU&list=PL86281C72D802CE05&index=66&feature=plpp_video


 

Ch 5.3  Sum and Difference Identities for Cosine

Sum and Difference Identities for Cosine :

Finding cos(A+B) if A=  in Quadrant II and B=  in Quadrant I
Determining the Exact Value of cos15°
Determining the Exact Value of cos
Determining the Exact Value of cos40°cos50°–sin40°sin50°
http://www.youtube.com/watch?v=H-0jQTzfkWQ

Verifying Sum Identity for Cosine (2nd Example in the Video) :

cos(x+ )= (cos(x) – sin(x))
http://www.youtube.com/watch?v=FRNiVsS5bVc

Finding the function values and the Quadrant of A–B :

Finding cos(x–y) from tan(x)=  and cos(y)=  Where x and y Are in Quadrant IV
http://www.youtube.com/watch?v=yklLtxBOb4s&feature=player_embedded

 

Cofunction Identities :

sin18º; tan65º, csc84º
cos( ); cot( ); sec( )
http://www.youtube.com/watch?v=_gkuml–4_Q&feature=youtu.be

 

Cofunction Identities : Solving Trigonometric Equations :

cos (2θ+16°)=sin(θ+11°)
cot(θ)=tan(θ+ )
http://www.youtube.com/watch?v=S4D-0ykqL_8&feature=youtu.be

 

 

Ch 5.4  Sum and Difference Identities for Sine and Tangent

 

Sum and Difference Identities for Sine :

Finding sin(A–B) from sin(A)=  in Quadrant II and cos(B)=  Quadrant III
Determining the Exact Value of sin105°
Determining the Exact Value of sin( )
http://www.youtube.com/watch?v=hiNDDQyee2E

 

Determining the Exact Value of sin75°
http://www.youtube.com/watch?v=NZ2Y5_XxzTc&feature=player_embedded

Determining the Exact Value of sin20°cos40°–cos20°sin40°-
http://www.youtube.com/watch?v=TNcNvSCBD30&feature=player_embedded

 

 

Sum and Difference Identities for Tangent  :

Determining the Exact Value of tan(–105°)
Determining the Exact Value of tan( )
Using an Identity to Write tan(π–θ) as a Single Function of θ
http://www.youtube.com/watch?v=OQP78bwYcWw

Determining the Exact Value of tan( )
http://www.youtube.com/watch?v=BuIhkzkJseM

 

Sum and Difference Identities to Simplify an Expression :

Simplify tan(x+4π)
http://www.youtube.com/watch?feature=player_embedded&v=7fy2U0Sm1Vc

Simplify tan(4π–x)
http://www.youtube.com/watch?v=75PmzAEO89A&feature=player_embedded

 

 

 

Finding the function values and the Quadrant of A+B :

Finding tan(2x) if sin(x)=  and x is in Quadrant I
http://www.youtube.com/watch?v=CvKaolqn2-Q&feature=player_embedded

Finding sin(2x) if tan(x)=  and x is in Quadrant I
http://www.youtube.com/watch?v=G4s7ui6HmRY&feature=player_embedded

 

 

 

 

Ch 5.5  Double-Angle Identities

 

Double Angle Identities :

Finding the Exact Value of cos(2A), sin(2A) and tan(2A) and Quadrant of 2A  if  sin(A)=  is in Quadrant II
Finding cos(A) given cos(2A)=  where 2A is in Quadrant III
http://www.youtube.com/watch?v=-zhCYiHcVIE

 

Using Double Angle Identities to Simplify and then Evaluate :
cos2( )–sin2( )
2sin( )–cos( )
2cos2( )–1
http://www.youtube.com/watch?v=Ukq-9RzR5-M

 

Example : Determining Double Angle Trigonometric Function Values with Given Quadrant :

Finding sin(2θ), sin(2θ) and tan(2θ) from cos( ) and θ is in Quadrant II
http://www.youtube.com/watch?v=Mkglhc1wYYo

 

Finding sin(2θ), sin(2θ) and tan(2θ) from tanθ=( ) and sinθ<0
http://www.youtube.com/watch?v=uI_vx1qhruM

 

Verifying Double Angle Identity (1st Example in the Video) :

(sinA+cosA)2= sin(2A)+1
http://www.youtube.com/watch?v=FRNiVsS5bVc

 

Example: Using Double Angle Identity :

1–16sin2x·cos2x
http://www.youtube.com/watch?v=eQW9a24flZA&feature=player_embedded

 

Product to Sum and Sum to Product Identities :

Product to Sum: sin(–4θ) sin(8θ)
Product to Sum : 2cos(  )–cos(  )
Product to Sum : sin(  )–cos(  )
Sum to Product :cos(9x)+cos(4x)
Sum to Product : sin( )–sin( )
http://www.youtube.com/watch?v=ps4Z01gFOpM

 

 

 

 

Ch 5.6   Half-Angle Identities

Half Angle Identities  :

Finding the Exact Value of sin(  )
Determining the Exact Value of cos105°
Finding cos( ), sin( ) and tan( ) from cosA=( ) in Quadrant II
http://www.youtube.com/watch?v=Rp61qiglwfg

 

Example: Rewriting a Trig Expression Using a Half Angle Identity :

(sin(5x))2
(cos(2x))4
http://www.youtube.com/watch?v=x6pfqRQ89fA

 

Example: Determine a Cosine Function Value Using a Half Angle Identity :

cos( )
http://www.youtube.com/watch?v=zaywBux2dv4

 

Example: Determining a Sine Function Value Using a Half Angle Identity :

sin(112.5°)
http://www.youtube.com/watch?v=q4XvvKKGhTc

sin(22.5°)
http://www.youtube.com/watch?feature=player_embedded&v=uFbbF-IYFjM

 

Example: Finding a Sine Function Value from a Cosine Function Value Using a Half Angle Identity :
Finding sin( ) if cos(a)=( ) for 0°≤a≤90°
http://www.youtube.com/watch?feature=player_embedded&v=FFXaeJYaGVY

 

Example: Determining a Tangent Function Value Using a Half Angle Identity :

tan( )
http://www.youtube.com/watch?v=Nks0B4XB4QA

tan(105°)
http://www.youtube.com/watch?feature=player_embedded&v=Q48HHoLauyg

 

Verifying Half Angle and Double Angle Identities for Sine (3rd Example in the Video) :
http://www.youtube.com/watch?v=FRNiVsS5bVc

 

 

 

 

 

 

Ch 6  Inverse Circular Functions and Trigonometric Equations

 

Ch 6.1  Inverse Circular Functions

Inverse Functions
http://www.youtube.com/watch?v=qgezKpQYH2w

Animation: Illustrate why a function must be one-to-one to have an inverse function
http://www.youtube.com/watch?v=UKhwZbgaT5M

 

Introduction to Inverse Sine, Inverse Cosine, and Inverse Tangent
http://www.youtube.com/watch?v=LUpa5nPskAc

 

Introduction to Inverse Cosecant, Inverse Secant, and Inverse Cotangent :

The Domain of y=sin(x) is [ , ] and the Range is [–1, 1]
The Domain of y=sin-1(x) is [–1, 1] and the Range is [ , ]
The Domain of y=cos(x) is [0, π] and the Range is [–1, 1]
The Domain of y=cos-1(x) is [–1, 1] and the Range is [0, π]
The Domain of y=tan(x) is [ , ] and the Range is [–∞ ∞]
The Domain of y=tan-1(x) is [–∞, ∞] and the Range is [ , ]
Finding the Exact Value of y=arcsin( )
Finding the Exact Value of y=arccos( )
Finding the Exact Value of y=tan-1(–1)
http://www.youtube.com/watch?v=IikDBR6T1zQ

 

Finding the Exact Inverse Function Values Involving Inverse Sine, Inverse Cosine, and Inverse Tangent :

Evaluating y=sin-1( )
Evaluating y=cos-1(0)
Evaluating y=arctan(–1)
http://www.youtube.com/watch?v=7Wd64tsv-O8

Evaluating y=sin-1(sin( ))
Evaluating y=sin-1(cos( ))
Evaluating y=tan-1(sin( ))
http://www.youtube.com/watch?v=4byJuNg5gKI

 

 

Finding the Exact Inverse Function Values Involving Inverse Cosecant, Inverse Secant, and Inverse Cotangent  :

Evaluating csc-1( ) in Degree and Radian
http://www.youtube.com/watch?v=ovYyPd5-rmk&feature=youtu.be

Evaluating arcsec(–2) in Degree and Radian
http://www.youtube.com/watch?v=rNp0JEZ3Rck&feature=youtu.be

Evaluating sin-1( )
Evaluating sec-1(2)
Evaluating csc-1( )
Evaluating cot-1(–1)
http://www.youtube.com/watch?v=5SX6Ghw9H3k

Evaluating csc-1(–√2) in Radian
Evaluating sec-1(–2) in Radian
Evaluating cot-1(√3) in Radian
http://www.youtube.com/watch?v=1jV953UFX8c

 

Determining the Exact Value without a Calculator (Part 1 of the video) :
arcsec(2)
arccsc( )
arccot(–1)
http://www.youtube.com/watch?v=w_PNSXTAMSw

 

Finding a Inverse Cotangent Value in Degrees and Radians Using a Calculator :

arccot(–3.5)
http://www.youtube.com/watch?v=K6uQ95vd3uE&feature=youtu.be

arccot(–3.6)
http://www.youtube.com/watch?v=cE3UKWhwZ6Q

 

 

Finding the Exact Function Values Involving Inverse Sine, Inverse Cosine, and Inverse Tangent :

sin(arccos( ))
cos(arctan( ))
sin(sin-1( )+tan-1(√–3))
Finding the Angle the Ladder Makes with the Ground
Finding the Maximum Angle of Elevation to Maximize a Shot Putter Distance
http://www.youtube.com/watch?v=Bq8WOgHxUFE

Evaluating sin(sin-1( ))
Evaluating cos(cos-1( ))
Evaluating tan(cos-1( ))
http://www.youtube.com/watch?v=4qO0qUqBQEU

Evaluating tan(sin-1( ))
http://www.youtube.com/watch?v=JFrBCBJMwos

Evaluating sin(tan-1(–7))
http://www.youtube.com/watch?v=6p2z58iUr10

Evaluating sin(tan -1( )) and Assume u>0
http://www.youtube.com/watch?v=WOWQy3YaTIY

 

Finding an Exact Sine Function Value Containing an Inverse Cosine – Double Angle :
sin(2arccos( ))
http://www.youtube.com/watch?v=Y7jm81eKVuI&feature=youtu.be

 

Finding the Exact Function Values Involving Inverse Cosecant, Inverse Secant, and Inverse Cotangent  Without a Calculator (Part 2 of the video) :
csc(arccot(u))
cos(sec-1( ))
sec(arccot( ))
http://www.youtube.com/watch?v=w_PNSXTAMSw

 

 

Ch 6.2  Trigonometric Equations I

Solving a Trigonometric Equation by Linear Method :

Solving Each Equation on the Interval [0, 2π) and then Over All Radian Solutions
2sinθ–1=0
2cosθ+√2=0
√3tanθ–1=0
4cosθ–6=cosθ
http://www.youtube.com/watch?v=26EWKD2Xha4

Solving sin(x)+ =0 on the Interval [0, 360°)
http://www.youtube.com/watch?v=LgSML90jjVU

Solving 2cos(x)sin(x)=sin(x) on the Interval [0, 360°)
http://www.youtube.com/watch?v=NFmIR_2FSgk

Solving 3tan2(x)–1=0 on the Interval [0, 2π)
http://www.youtube.com/watch?v=KIHrcxj_Guw

Solving 3=20sin(x–3)+1 on the Interval [0, 2π) (Part 1 of the video)
http://www.youtube.com/watch?v=GqVopraSumU

Solving  on the Interval [0, 2π) (Part 1 of the video)
http://www.youtube.com/watch?v=Qc-W3TaTFc8

 

Example: Solving Trigonometric Equation: sin(x)=cos(x)
http://www.youtube.com/watch?v=ww5pnpVGejk

 

 

Solving a Trigonometric Equation by Factoring :

Solving tan2θ–1=0 on the Interval [0, 2π)
Solving 2cos2θ–√3cosθ=0 on the Interval [0, 2π)
Solving 2sin2θ=–3sinθ–1 on the Interval [0, 2π)
http://www.youtube.com/watch?v=ABKO3ta_Azw

Solving 2cos2(x)–sin(x)=1 on the Interval [0, 2π)
http://www.youtube.com/watch?v=JtPhE_Qu0A8

Solving cos2(x)–cos(x)–2=0 on the Interval [0, 2π)
http://www.youtube.com/watch?v=3UjZ6tmgpYw

Solving a Trigonometric Equation by Trigonometric Identities :

Solving cos2(x)–sin2(x)=  on the Interval [0, 360°)
Solving tanθ+√3=secθ on the Interval [0, 2π)
http://www.youtube.com/watch?v=7thuFLqC7z0

Solving sec2(x)–2tan(x)=4 on the Interval [0, 2π) (Part 2 of the video)
http://www.youtube.com/watch?v=Qc-W3TaTFc8

 

Solving a Trigonometric Equation Using the Calculator :

Solving sin(x)–0.32=0 on the Interval [0, 2π)
http://www.youtube.com/watch?v=E7Y5SixiBpI

Solving cos(x)+0.85=0 on the Interval [0, 2π)
http://www.youtube.com/watch?v=9KfOp7uKRHs

 

Solving Applications Problems :

The Function T(x)=19sin( x – )+53  Modeling the Average Monthly Temperature of Water in a Mountain Stream
The Function S(x)=1600cos( x+ )+5100 Modeling the Average Monthly Sales in the Month x
http://www.youtube.com/watch?v=VUnmOqSEAO0

 

Determining the Height of an Object Using a Trigonometric Equation
http://www.youtube.com/watch?v=-2w7Mdq5C58

 

 

 

 

Ch 6.3  Trigonometric Equations II

Solving a Trigonometric Equation by Double Angle :

Solving cos(2x)+sin2(x)–3cos(x)=1 on the Interval [0, 360°) (Part 3 of the video)
http://www.youtube.com/watch?v=7thuFLqC7z0

Solving cos(2θ)–cos(θ)=0 on the Interval [0, 2π)
Solving sin(θ)–sin(2θ)–=0 on the Interval [0, 2π)
http://www.youtube.com/watch?v=8FRly0POPD8 (Part 3 and 4 of the video)

Solving sin(2x)=cos(2x)+1 on the Interval [0, 2π) (Part 3 of the video)
http://www.youtube.com/watch?v=Qc-W3TaTFc8

Solving cos(2x)=cos(x) on the Interval [0, 2π)
http://www.youtube.com/watch?v=xqbMviYLy_k

Solving sin(2x)=2cos2(x) on the Interval [0, 2π)
http://www.youtube.com/watch?v=9mfvng-9cr0

 

Solving a Trigonometric Equation by Half Angle (Part 1 of the video):
sin( )=√2–sin( )
http://www.youtube.com/watch?v=8FRly0POPD8

 

Solving a Multiple-Angle–Trigonometric Equation by Single Angle :

Solving 4cos(4x)=2 on the Interval [0, 2π)
http://www.youtube.com/watch?v=iQVKysQp_1s

Solving 5sin(3x)=2 on the Interval [0, 2π)
http://www.youtube.com/watch?v=WmHHPapOSok

Solving 2cos(3x)–√3=0 on the Interval [0, 360°) (Part 2 of the video)
http://www.youtube.com/watch?v=8FRly0POPD8

 

 

 

 

Ch 6.4  Equations Involving Inverse Trigonometric Functions

Solving the Equation for Secant x :
√5+2sec(3x)=y
http://www.youtube.com/watch?v=j1NQnYBu4ZQ

 

Solving a Trigonometric Equation with an Inverse Trig Function :

4arctan(x)=π
cos-1(x)=sin-1( )
http://www.youtube.com/watch?v=GqVopraSumU  (Part 2 and 3 of the video)

cos-1( )=( )
http://www.youtube.com/watch?v=Ym3Rrnk2o5k

cos-1( )=π
http://www.youtube.com/watch?v=V_iF8bprCrE&feature=youtu.be

cos-1(x)=sin-1( )
http://www.youtube.com/watch?v=zeO4A6w51cI&feature=youtu.be

 

 

 

 

 

Ch 7  Applications of Trigonometry and Vectors

 

Ch 7.1  Oblique Triangles and the Law of Sines :

The Law of Sines: The Basics :
Solving the Triangle with A=48°, B=54°, a=12.5feet
http://www.youtube.com/watch?v=dxYVBbSXYkA

Solving the Triangle with C=102°, b=5m, c=18m
http://www.youtube.com/watch?v=LzdDALbFlxY

 

The Law of Sines: Applications :

Finding the Distance Across the Canyon
http://www.youtube.com/watch?v=VqapJYCG31k

Finding the Distance of the Campsite from the Base of the Mountain and the Time Needed to the Base
http://www.youtube.com/watch?v=az3JAqNMGt4

Determining the Length of x
http://www.youtube.com/watch?v=9l23gPNAs_g

Determining the Distance from the Tower to the Airplane
Determining the Elevation of the Airplane
http://www.youtube.com/watch?v=6dEvIdTJ708

 

The Area of a Triangle using Sine :

Determining the Area of a Triangle with A=35°, B=82°, a=6cm, b=15cm
Determining the Area of a Triangle with B=72°, a=23.7ft, b=25.2ft
http://www.youtube.com/watch?v=mBFDq4bPXMs

 

 

 

 

Ch 7.2  The Ambiguous Case of the Law of Sines

The Law of Sines: The Ambiguous Case :

Solving the Triangle with C=82°, a=11m, c=7m
Solving the Triangle with A=88°, a=110ft, c=54ft
Solving the Triangle with B=40°, b=22cm, a=30cm
http://www.youtube.com/watch?v=ETqe-_plC3Y

 

 

 

Ch 7.3  The Law of Cosines

The Law of Cosines :

Solving Triangle ABC with B=73.1°, a=24.2ft, c=43.7ft
Solving Triangle ABC with a=25.4cm, b=42.8cm, c=59.3cm
http://www.youtube.com/watch?v=hBzKRHH_grk

 

The Law of Cosines: Applications – Determining a Side from Two Sides and an Angle :

Determining the Diagonal of a Parallelogram
http://www.youtube.com/watch?v=_NyWGW6Pu1w

Determining the Length of the Tunnel and the Bid Amount after 20% profit off the Cost
Determining the Duration of Service a Person gets when She is Driving Past a Transmission Tower at a Certain Speed
http://www.youtube.com/watch?v=1SvHQNBGU6Q

Determining the Flying Distance of A plane From Her Starting Position
http://www.youtube.com/watch?v=wu29Zdk_PZA

The Law of Cosines: Applications – Determining the Largest Angle of the Three Sides
http://www.youtube.com/watch?v=-U97mrpL_aE

 

Heron's Area Formula :

Determining the Areas of Triangles Using Heron’s Area Formula
http://www.youtube.com/watch?v=Pi56pFy-8HU

 

 

 

 

 

Ch 7.4  Vectors, Operations, and the Dot Product

Introduction to Vectors :
http://www.youtube.com/watch?v=IKzR0Odurm0

 

Vector Basics – Drawing Vectors/ Vector Addition
http://www.youtube.com/watch?feature=player_embedded&v=pimr9I92GZY

 

Finding the Components of a Vector :

Finding x and y Components of a Vector with a Magnitude of 8 and at an Angle of 60° from the Origin
http://www.youtube.com/watch?feature=player_embedded&v=-fbCI2qcgRk

Finding x and y Components of Vectors
http://www.youtube.com/watch?v=R9f1t-OP358&feature=player_embedded

 

Vector Basics - Algebraic Representations :

Drawing the Vector =<2,3>
Drawing the Vector   =<–3,4>
Finding the Vector  of (2, 1) and (5, 6)
http://www.youtube.com/watch?v=odhAVmAahb4&feature=player_embedded

Adding + +  where =<2, 2>, =<3, 0> and =<0, –6>
Multiplying 10  where =<1, 4>
Simplifying –2  where  =<1,4> and =<–2, 3>
http://www.youtube.com/watch?feature=player_embedded&v=IUzoNG4-MIc

 

Magnitude and Direction of a Vector :

Finding the Magnitude and Direction of Vector <–3, 4>
http://www.youtube.com/watch?v=WxWJorOVIj8&feature=player_embedded

Finding the Magnitude and Direction of Vector <–2, –5>
http://www.youtube.com/watch?v=-gokuNjpyNg&feature=player_embedded

Finding the Magnitude and Direction of Vector <2, 6> and <3, –10>
http://www.youtube.com/watch?v=ZDMm8mtDWhE&feature=player_embedded

 

The Dot Product :

Finding ·  where =<2, 5> and =<–3, 1>
Finding the Angle of =6i–2j–3k and =i+j+k
Determining if =<2, 4> and =<4, –2> are Orthogonal
http://www.youtube.com/watch?v=98C7iv8OcnI&feature=player_embedded

 

 

 

Ch 7.5  Applications of Vectors

Vectors: Applications :

Finding the Distance between the Ship and the Port and its Bearing
Finding the Direction and Magnitude of the Resultant Force of Two Trucking Pulling on a Truck Stuck in the Mud
http://www.youtube.com/watch?v=53UdTRt_re0

 

 

 

 

 

Ch 8  Complex Numbers, Polar Equations, and Parametric Equations

 

Ch 8.1  Complex Numbers

Introduction to Complex Numbers :

Solving x2–10x+34=0
Simplifying Complex Number in the Form of a+bi
http://www.youtube.com/watch?v=NeTRNpBI17I

 

Complex Number Operations :

Adding (3+4i)+(7–5i)
Adding (–2+7i)–(–4+7i)
Multiplying (2+3i)(3–4i)
Multiplying (5–2i)2
Multiplying (7+2i)(7–2i)
Performing i5
Performing i24
Performing i35
Dividing
Dividing
http://www.youtube.com/watch?v=htiloYIILqs

 

Rewriting Powers of ‘i’ :

Simplifying i8; i12; i16; i20
Simplifying –i42; i31; i–42; i–28; – i–13
http://www.youtube.com/watch?v=VTAsbx5wBaI&feature=player_embedded

Simplifying i–42; i–28; – i–13
http://www.youtube.com/watch?feature=player_embedded&v=tbWfxuV-IeE

 

 

 

Ch 8.2  Trigonometric (Polar) Form of Complex Numbers

Trigonometric Form z=r(cosθ+i sinθ) of Complex Numbers :

Plotting 2+3i; 4i; –3; –1–4i
Graphing z=12(cos +i sin ) and Converting it to Rectangular Form
Graphing z=3csi150° and Converting it to Rectangular Form
Writing z=–2+2i in Trigonometric Form
Writing z=3+5i in Trigonometric Form
http://www.youtube.com/watch?v=Zha7ZF8aVhU

 

Converting from Rectangular Form to Trigonometric Form z=x+yi :

Converting 2+2i into Polar Form
http://www.youtube.com/watch?feature=player_embedded&v=6z6fzPXUbSQ

Converting –4i into Polar Form
http://www.youtube.com/watch?v=tAIxdEVuTZ8&feature=player_embedded

Converting (3–i)2 into Polar Form
http://www.youtube.com/watch?v=XIYDO_weAVA&feature=player_embedded

 

Converting from Trigonometric Form to Rectangular Form :

Converting 3(cos135°+i sin135°) to Complex Form
Converting 4(cos270°+i sin270°) to Complex Form
http://www.youtube.com/watch?v=tl56MgKA3Z8&feature=player_embedded

 

 

 

 

Ch 8.3  The Product and Quotient Theorems

The Product and Quotient of Complex Numbers in Trigonometric Form :

Multiplying [2(cos +i sin )][3(cos +i sin )]
Dividing
http://www.youtube.com/watch?v=JNiLUgJcluU

Dividing
Multiplying [2(cos45°+i sin45°)][5(cos30°+i sin30°)]
http://www.youtube.com/watch?v=in_dAlpjUKk&feature=player_embedded

Dividing
http://www.youtube.com/watch?feature=player_embedded&v=QxboPshf__g

 

 

 

 

Ch 8.4  De Moivre’s Theorem; Powers and Roots of Complex Numbers

 

De Moivre’s Theorem : Raising a Complex Number to a Power :

Rewriting [2(cos +i sin )]3 in Rectangular Form
Using De Moivre’s Theorem to Compute ( – i)5
http://www.youtube.com/watch?v=Sf9gEzcVZkU

 

Using De Moivre’s Theorem to Compute (2+2i)4(√3+i)2
http://www.youtube.com/watch?v=irwItP7PiQg&feature=player_embedded

 

Determining the nth Roots of a Complex Number :

Determining all 4th Roots of z= –8+8i √3
http://www.youtube.com/watch?v=0Gyv9ce7f8I

 

 

 

 

Ch 8.5  Polar Equations and Graphs

Introduction to Polar Coordinates :

Plotting P(3, 30°), Q(2, ), R(–4, 60°), S(–1, – ) on the Polar Coordinate System
Listing the Given Point in a 4 Different Way on the Polar Coordinate
Listing A(–1, –1) in a 2 Different Way on the Polar Coordinate
Writing E(–1, ) in Rectangular Coordinate
http://www.youtube.com/watch?v=-tZR3ggdoIU

 

Listing the Given Point in a 4 Different Way on the Polar Coordinate in Degrees
http://www.youtube.com/watch?v=ds-YLa7Yd0k

 

Listing the Given Point in a 4 Different Way on the Polar Coordinate in Radians
http://www.youtube.com/watch?v=0xh32SzuUSU

 

Animation: Comparing Polar and Rectangular Coordinates
http://www.youtube.com/watch?v=A-AEuohaP4o

 

Converting (4, 1) and (–2, 3) to Polar Coordinates Using Degrees
http://www.youtube.com/watch?v=Vg88CWOlDTY

 

Convert (–3, 3) and (–4, –3) to Polar Coordinates Using Radians
http://www.youtube.com/watch?v=_rSC6Im1u1U

 

Finding the Rectangular and Polar Equation of a Circle from a Graph
http://www.youtube.com/watch?v=ZFNSMfWvVNY&feature=youtu.be

 

Finding the Polar Equation for a Horizontal Line
http://www.youtube.com/watch?v=_Ku4ZP4bmps&feature=youtu.be

 

Writing the Equation Line 3x–2y=6 in Polar Form
http://www.youtube.com/watch?v=xrsJNoq4oN4&feature=youtu.be

 

Graphing Polar Equations :
r=3
θ=
r=3sinθ
r=3cosθ
http://www.youtube.com/watch?v=X6M7yfH6w_Y

r=4sin(3θ)
Showing Circles, Lemniscates, Limacons, and Rose Curves
http://www.youtube.com/watch?v=mTxxNQWWlBc

 

Graphing Polar Equation y=3cos(2θ): Part 1 and 2
http://www.youtube.com/watch?v=mDT_DG_A0JA&feature=player_embedded
http://www.youtube.com/watch?v=GMcRqtm4mNo&feature=player_embedded

 

 

Graphing Polar Equation y=4sin(3θ) on the TI84 Graphing Calculator
http://www.youtube.com/watch?v=PZwiiZQhM0c&feature=youtu.be

 

Converting Polar Equations to Rectangular Equations and Graphing them :
r=tanθsecθ
r=4cosθ
r=
http://www.youtube.com/watch?v=IKbRiU7kL2w

 

Converting Rectangular Equation r sin2(θ)=2cos(θ) to Polar Equation and Graphing them
http://www.youtube.com/watch?v=A1y81g78VoM&feature=youtu.be

 

 

 

Ch 8.6  Parametric Equations, Graphs, and Applications

Parametric Curves – Basic Graphing :

Sketching the Curve Given by x=1–t , y=t2; –2≤t≤2
Sketching the Curve Given by x=2t–2, y= –t+3
Sketching the Curve Given by x=4–6t, y=3t
Sketching the Curve Given by x=2t, y=t2+1, –∞≤t≤∞
http://www.youtube.com/watch?v=VqsGKIWsT20

Sketching the Curve Given by x=1+√t, y=t2–4t, 0≤t≤5
Sketching the Curve Given by x=√t, y=1–t
http://www.youtube.com/watch?feature=player_embedded&v=tsnHL1Lb5MU