Download PreCalc Ch 6- Notes 6.1

Precalculus: Chapter 6
Notes: Section 6.1
Objectives: Evaluating Trigonometric Expressions Using Identities
Using Law of Sines to Solve Oblique Triangles- SAS and AAS
Finding Area of Oblique Triangles
Applications of Law of Sines
Ambiguous Case- SSA
Law of Sines:
sin A sin B sin C


a
b
c
EX: Use the information to solve each triangle.
1. A = 60, a = 9, b = 10
Sum and Difference Identities:
2. A = 5 degrees 40 minutes
B=
sin( u  v)  sin u cos v  cos u sin v
tan( u  v) 
cos(u  v)  cos u cos v  sin u sin v
tan u  tan v
1  tan u tan v
EX: Find the exact value of the trigonometric function given that sin u  
12
4
and cos v   . (Both u
13
5
and v are in Quadrant III.)
2. cscu  v
3. cotv  u 
sin 2u  2 sin u cos u
cos 2u  cos 2 u  sin 2 u
cos 2u  2 cos 2 u  1
cos 2u  1  2 sin 2 u
tan 2u 
1.
cosu  v 
Double Angle Identities:
2 tan u
1  tan 2 u
EX: Find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas.
1.
cos u 
4
,
5
3
 u  2
2
2. cot u  3 ,

2
u 
Half Angle Identities:
sin
u
1  cos u

2
2
cos
u
1  cos u

2
2
tan
EX: Use the figure to the right to find the
exact value of the trigonometric function.
1.
sin
3.
sec

2

2
2. tan

2
u 1  cos u
sin u


2
sin u
1  cos u