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 = 6, 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
 3

 3

trigonometric function): sin 
 x   sin 
 x
 2

 2

Mathematical Investigations IV
3. (5 pt) Prove: tan( ) 
Name:
1  cos(2 )
sin(2 )
4.(5 pts) If ABC has sides, a  5, b  7, and c  9 , find the values (in degrees, to nearest tenth of a
degree) of the angles A, B, and C .
Mathematical Investigations IV
Name:
3
1


5. (2 pt each) If sin     , cos     , 0    , and     determine exact values for each of
5
2
2
2
the following:
a. cos 
b. sin  
c. cos(   ) =




d. sin  2  
ptSolve the equation for 0    2 (you must show all work without aid of calculator):
2sin 2   3  9cos( )
Mathematical Investigations IV
Name:
7. (4 pt) Mr. Stalmack wishes to find the height of the Willis Tower, which he still calls the Sears
Tower. He stands on the ground some distance away from the tower and observes that the angle of
elevation to the top of the building is 70 . He walks 100 feet closer to the tower and the angle of
elevation is now 73.6 . How tall (in feet) is the Willis Tower?
8. (4 pt) Suppose a square and a regular hexagon share a side. If the area of the square is
the area of the hexagon.
3 un2, find