Mathematical Investigations IV
Name:
Trigonometry Exam
With Calculator
Instructions: Answers without work will receive little or no credit. You must show sufficient work on
all problems so that I can reproduce your results. If any problem has multiple solutions, be sure you
clearly indicate which values go together. Unless otherwise stated, calculators may only be used to
compute numerical values of built-in functions.
1. (5 pt) Given DEF with e = 10, d = 7.3, and mE  32 , solve for side f . Round final answers to
two decimal places.
2. (4 pt) Simplify (answer should be simplified so as to involve a single term involving one
2
trigonometric function): 1  sin 2 x  
1  tan 2 x 
Mathematical Investigations IV
3. (5 pt) Prove: cot( x) 
Name:
sin(2 x )
1  cos(2 x )
4.(5 pts) If ABC has an area of 12, a  5, and b  7, solve for  C
Mathematical Investigations IV
Name:
3
5 
3
5. (2 pt each) If sin     , cos    
determine exact values for each
,
   , and    
5
13 2
2
of the following:
a. cos 
b. sin  
c. cos(   ) =




d. csc  2 
ptSolve the equation for 0    2 (you must show all work without aid of calculator):
sin 2  2 cos
Mathematical Investigations IV
7. (4 pt) Solve for x: sin(cos1 ( x )) 
Name:
x
2
8. (4 pt) In the figure at the right, determine the length of AC.
A
12
8
B
7
C
10
D