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Math 110 Trigonometric & Analytic Geometry
Test #1
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All questions are 10 points each
1.
a) Convert the angle
225 to
radians
b) Find one positive and one negative angle that is coterminal with the angle
2. Find the exact values for the six trigonometric functions of
4
3

1
3. Find the exact value of each of the remaining trigonometric functions of a positive angle  .
Given that
cos   
4.
12
13
Given that  
and

3
2
. Draw the angle first.
11
6
a) Find the reference angle for  .Draw the angle and the reference angle
b) Use the reference angle to find the exact value (Do not use a calculator) of
cos
11
6
2
5.
Given that point
(1, 3) is the on the terminal side of a positive angle 
. Find the exact
value of each of the six trigonometric functions of  . You must draw the angle first.
6.
A ceiling fan with 16-in. blades rotates at 45 rpm. (Round your answer to one decimal
place.)
a.
Find the angular speed of the fan in rad/min.
b. Find the linear speed of the tips of the blades in in/sec.
c. Find the linear speed of the tips of the blades in mile/hour.
3
7. A water tower is located 325 ft from a building (see the figure). From a window in the

building, an observer notes that the angle elevation to the top of the tower is 39 and that the

angle of depression to the bottom of the tower is 25 . How tall is the tower?
8. Solve the triangle. Given that a = 21, b = 30, c = 24
Then find the area for the above triangle. (Round your answer to one decimal place)
4
9. Find the exact value for. Do not use a calculator.
a.
b.
2 cos 45  4 sin 30 
1


 sin 2  4 cos
4
6
3
10. Find the exact value for. Do not use a calculator
a.
 
sin 1 sin 
 3
b.

5

cos tan 1
2


5