Trig Exam F12
Name:__________________
You may use the TI-30 calculator. All steps leading to your solution should be clearly shown.
True and False (2 pt each)
  2
_____ 1. sin 1  sin 
  3
 
  .
 3
_____ 2. 1  2sin 2   2 cos 2   1 .
_____ 3. Given any triangle ABC, a  sin C  c  sin A .
_____ 4. Given any triangle ABC, a 2  b 2  c 2  2bc cos C .
_____ 5. The domain of g ( x)  tan 1 x is (1,1) .
6. (5 pt) If sin   
2
3
and    
, find the exact value of each expression:
3
2
a. cos  
2 

c. cos   

3 

b. cos  2 
Trig Exam F12
Name:__________________
7. (5 pt) Find all solutions (if any) to ΔABC if a  3 , b  4 , and A  40 . Give answers to one
decimal place.
8. (4 pt) Simplify: csc  1  cos(2 ) 
9. (6 pt) Find all solutions to: cos(2 x)  1  sin x .
Trig Exam F12
10. (10 pt) Prove each identity:
a.
1  cos(2 )
 tan 
sin(2 )


sin  x  
2

 1
b.
cos( x)
Name:__________________
Trig Exam F12
Name:__________________
11. (4 pt) Find the area of the regular pentagon inscribed in a circle of radius 8. Note that a
regular pentagon has five equal sides and five equal angles.
12. Find the angles of ABC if the three sides are a  7, b  7, and c  9.