PreCalc Chapter 7

Ch 7 Applications of Trigonometry

Ch 7.1 Law of Sines

Definition of Law of Sines ;
Introducing ASA, SAS, SSS, AAA and SSA;
Finding c given A=123°, B=41°, a=10;
Solving Triangle given A=95°, C=68°, b=115 yards ;
Concept of One or Two Solutions of SSA Triangle
http://www.youtube.com/watch?v=5um1IU0HTTI&list=PL554F9F460401DF50&index=43&feature=plpp_video

Solving SSA (Side, Side, Angle) Triangle given A=26°, a=21ft,  b=5 ft;
Finding C given B=78°, b=5, c=12 for SSA Triangle ;
Finding B given A=29°, a=6, b=12 for SSA Triangle ;
Solving the Word Problem : Finding the Distance of the Fire from One of the Two Towers
http://www.youtube.com/watch?v=boE-K16AAAs&list=PL554F9F460401DF50&index=42&feature=plpp_video

Solving ASA (Angle, Side, Angle) Triangle given A=60°, c=90, B=40°
http://www.youtube.com/watch?v=8mA_VNBrbqw&feature=plcp

Solving SSA (Side, Angle, Angle) Triangle given b=40, A=43°, B=62
http://www.youtube.com/watch?v=YZVXk1pBFrs&feature=plcp

Solving  SSA (Side, Side, Angle) Triangle (Ambiguous Case) with One solution given a=76, c=52, A=39°
http://www.youtube.com/watch?v=CXU-zGTfHGM&feature=plcp

Solving SSA (Side, Side, Angle) Triangle (Ambiguous Case) with Two solutions given a=52, b=63, A=42°
http://www.youtube.com/watch?v=sXn_rkJE3WI&feature=plcp

Solving SSA (Side, Side, Angle) Triangle (Ambiguous Case) with No solutions given a=48, c=68, A=86°
http://www.youtube.com/watch?v=u8zLE0buKPY&feature=plcp

Application : Finding the Length of the Guy Wire
http://www.youtube.com/watch?v=AMKNi204Hwg&feature=plcp

Ch 7.2 The Law of Cosines

Definition of Law of Cosines ;
Solving the Triangle given , ,  ;
Solving the Triangle given , ,  ;
Finding the Distance between the Ship and the Port ;
Finding the Area of a Triangular Region with Side ,  and  using Heron’s Area Formula  ;
Finding the Area of a Triangle given , ,
http://www.youtube.com/watch?v=bHk69ho59Ak&list=PL554F9F460401DF50&index=41&feature=plpp_video

Solving the Triangle using Law of Cosines given , ,
http://www.youtube.com/watch?v=wfbil5ybeXY&feature=plcp

Finding the Area of Oblique Triangle using formula  given  inch,  inch,
http://www.youtube.com/watch?v=7SPH72cskSA&feature=plcp

Ch 7.3 Vectors

Definition of Vectors ;
Showing u=v given u=  to  and v= to  ;
Finding Component Form and then Magnitude and Direction of the Vector from  to  ;
Finding 4uu+v ,  and  2uv  given u=  and v=  ;
Definition of i and j ;
Expressing v=  in terms of i and j ;
Finding the Direction and Magnitude of v=2ij ;
Determining if the Ramp would Support the Weight of the Piano
http://www.youtube.com/watch?v=Hy-KYbZ9CJo&list=PL554F9F460401DF50&index=40&feature=plpp_video

Adding, Subtracting, Scalar Multiples of Vectors v=3i+4j and w= 5i–2j
http://www.youtube.com/watch?v=0Vy8xGbH6EQ&feature=plcp

Finding the Unit Vector v= 8i–6j
http://www.youtube.com/watch?v=69ENDdvo8Yw&feature=plcp

Finding the Magnitude of Vector u from  to
http://www.youtube.com/watch?v=X58qqQoWEUU&feature=plcp

Finding the Velocity of the Plane as a Vector when Magnitude and Direction are given
http://www.youtube.com/watch?v=IJaLj_EYrpI&feature=plcp

Finding the Resultant Speed and Direction of the Plane
http://www.youtube.com/watch?v=2967YlfgBfs&list=PL554F9F460401DF50&index=39&feature=plpp_video

Ch 7.4 The Dot Product

Finding the Dot Product u·v and u·(v+w) Given u= , v=  and w=  ;
Angle Between Two Vectors ;
Parallel and Orthogonal Vectors ;
Finding the Angle Between u= , v=  ;
Determining if Two Vectors u= , v=  are Orthogonal ;
Definition of the Component of Vector a along Vector b ;
Definition of Work Done ;
Finding the Force required to Keep the Piano from Rolling Down the Ramp ;
Finding the Work Done needed for a Man to Push the Broom for a Distance
http://www.youtube.com/watch?v=c5mSscguIXg&list=PL554F9F460401DF50&index=38&feature=plpp_video

Finding the Dot Product of Two Vectors v=6i–2j and w= –4i+5j
http://www.youtube.com/watch?v=Yj7R13CUYNE&feature=plcp

Finding the Angle between Two Vectors v= –2i+3j and w=6i–2j
http://www.youtube.com/watch?v=K96bQZMUTyE&feature=plcp

Finding the Magnitude and Direction of the Resulting Force of Two Forces Acting on an Airplane
http://www.youtube.com/watch?v=X5xPr2WIboM&feature=plcp

Finding the Work needed to Push a Vehicle to the Gas Station
http://www.youtube.com/watch?v=UhKg-jSgsjk&feature=plcp

Ch 7.5 Trigonometric Form for Complex Numbers

Definition of Absolute Value of a Complex Number ;
Finding Absolute Value of  ;
Rectangular Form of Complex Numbers  ;
Trigonometric Form of Complex Numbers  ;
Exponential Form of Complex Numbers  ;
Writing in Trigonometric Form ;
Writing  in  Form ;
Multiplication and Division of Complex Numbers in Trigonometric Form ;
Multiplying and Dividing  and
http://www.youtube.com/watch?v=ZhvESftd5-A&list=PL554F9F460401DF50&index=37&feature=plpp_video

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

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

Converting  into Trigonometry/Polar Form
http://www.youtube.com/watch?v=XIYDO_weAVA&feature=player_embedded

Writing the Complex Number  in Polar Form
http://www.youtube.com/watch?v=qEp8mdgZazI&feature=plcp

Converting  to Rectangular Form ;
Converting  to Rectangular Form
http://www.youtube.com/watch?v=tl56MgKA3Z8&feature=player_embedded

Writing the Complex Number   in Rectangular Form
http://www.youtube.com/watch?v=9rxaasy96dw&feature=plcp

Ch 7.6 DeMoivre’s Theorem and nth Roots of Complex Numbers

Definition of DeMoivre’s Theorem ;
Evaluating  ;
Definition of Roots of Complex Numbers ;
Finding the First Fourth Roots of  in Rectangular Form  and Trigonometric Form  ;
Finding the First Third Roots of  in  Form and Trigonometric Form (Part 1)
http://www.youtube.com/watch?v=YLoSvy673L8&list=PL554F9F460401DF50&index=36&feature=plpp_video

Finding the First Third Roots of  in  Form and Trigonometric Form (Part 2) ;
Solving
http://www.youtube.com/watch?v=Al2_0OxsDKE&list=PL554F9F460401DF50&index=35&feature=plpp_video

Rewriting  in Rectangular Form ;
Using De Moivre’s Theorem to Compute
http://www.youtube.com/watch?v=Sf9gEzcVZkU

Using De Moivre’s Theorem to Compute
http://www.youtube.com/watch?v=irwItP7PiQg&feature=player_embedded

Determining all  Roots of
http://www.youtube.com/watch?v=0Gyv9ce7f8I