# 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

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

Solving ASA (Angle, Side, Angle) Triangle given A=60°, c=90, B=40°

Solving SSA (Side, Angle, Angle) Triangle given b=40, A=43°, B=62

Solving  SSA (Side, Side, Angle) Triangle (Ambiguous Case) with One solution given a=76, c=52, A=39°

Solving SSA (Side, Side, Angle) Triangle (Ambiguous Case) with Two solutions given a=52, b=63, A=42°

Solving SSA (Side, Side, Angle) Triangle (Ambiguous Case) with No solutions given a=48, c=68, A=86°

Application : Finding the Length of the Guy Wire

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 , ,

Solving the Triangle using Law of Cosines given , ,

Finding the Area of Oblique Triangle using formula  given  inch,  inch,

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

Adding, Subtracting, Scalar Multiples of Vectors v=3i+4j and w= 5i–2j

Finding the Unit Vector v= 8i–6j

Finding the Magnitude of Vector u from  to

Finding the Velocity of the Plane as a Vector when Magnitude and Direction are given

Finding the Resultant Speed and Direction of the Plane

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

Finding the Dot Product of Two Vectors v=6i–2j and w= –4i+5j

Finding the Angle between Two Vectors v= –2i+3j and w=6i–2j

Finding the Magnitude and Direction of the Resulting Force of Two Forces Acting on an Airplane

Finding the Work needed to Push a Vehicle to the Gas Station

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

Converting  into Trigonometry/Polar Form

Converting  into Trigonometry/Polar Form

Converting  into Trigonometry/Polar Form

Writing the Complex Number  in Polar Form

Converting  to Rectangular Form ;
Converting  to Rectangular Form

Writing the Complex Number   in Rectangular Form

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)

Finding the First Third Roots of  in  Form and Trigonometric Form (Part 2) ;
Solving