Trig Exam F12 α
Name:__________________
You may use the TI-30 calculator. All steps leading to your solution should be clearly shown.
True and False (2 pt each)
_____ 1. For any real number a, sin  sin 1  a    a .
_____ 2. sin 2  2   4sin 2   cos2  .


_____ 3. cos      sin  .
2

_____ 4. Given any triangle ABC, 1 
c  sin A
.
a  sin C
_____ 5. The domain of g ( x)  tan 1 x is  ,   .
6. (5 pt) If sin   
1
3
   2 , find the exact value of each expression:
and
5
2
a. cos  


c. sin    
3

b. cos  2 
Trig Exam F12 α
7. (4 pt) Simplify:
Name:__________________
1  cos(2 )
.
sin(2 )
8. (6 pt) Find all solutions to: cos(2 x)  1  sin x .
Trig Exam F12 α
Name:__________________
9. (10 pt) Prove each identity:
a.
cos( x  y )
 cot x  tan x
sin x  cos y
b. csc  1  cos(2 )   2sin
10. On a lazy Saturday afternoon, Dallas and Tony are watching Dr. Krouse climb the Willis
tower (formerly known as the Sears tower). When they look up to see Dr. Krouse, they note that
the angle of elevation is 28 . They walk 400 feet toward the building and now find that Dr.
Krouse hasn’t climbed at all and is now at an angle of elevation of 38 . How far up the building
has she climbed? That is, how high is she?
Trig Exam F12 α
Name:__________________
11. Find the angles of GAO if the three sides are g  7, a  8, and o  12.