Chapter 4 Trigonometry

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

Finding the Period of y=cos(3x), and y=sin(x/4 );

Finding and Graphing the Amplitude and Period of  y=sin( x/3), y= 1/2 cos(2x) and y= –2sin(3x)
http://www.youtube.com/watch?v=qJ-oUV7xL3w

Finding the Amplitude and Period of y= –4cos(3x), y=1/2 sin(x) and y= √2 cos(1/2 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 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

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

Graphing Vertical Translation of y=sin (x)+1 and y=cos(x)–1/2;

Graphing Horizontal and Vertical Translation for y=sin(x– ╥/4)+1, and y= – 1/2 +cos(x+ ╥/2)
http://www.youtube.com/watch?v=DswBtrtvR5M

Graphing Horizontal and Vertical Translation for y=1/2+sin(x+ ╥/4)
http://www.youtube.com/watch?v=Gu0vV73V-no

Graphing Sine and Cosine with Different Coefficients (Amplitude, period, and Vertical Translation) : y=2sin(1/2 ╥x )–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

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

y=2cos (x– ╥/2)+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 tan θ=(sin θ/cos θ)
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( x/4)
y=2tan(x/2 )
y=1/2 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

Graphing y=2cot(1/4 x) with Transformation
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

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