Trigonometry Review
Pre-Calc. for AP Prep.
Name: _________________
Date: _________________
No Calculators.
1. sin 240
 3 
2. sec  

 2 
3. tan(-390)
 17 
4. cot 

 6 
5. csc(840)
6. tan
 19 
7. sec  

 4 
8. sin 1 (1)
 2 3
9. csc 1  

3 


3
10. cot 1  

 3 


2 
11. sec  cos 1  
 2  





 1 
12. cos  cos 1   
 2 


 1 
13. sec  sin 1   
 x 

14. sin
37
6

 
 11 
cos 0  sin    cos 

4
 6
 3 
Find the exact values of the trigonometric functions based on the information provided.
15.   A  2 and secA =
34
16
sinA = _____ cosA = _____ tanA = _____
16.
If a regular hexagon with side length 10 3 is inscribed in a circle, how much
larger is the area of the circle than that of the hexagon?
17.
In the figure below, ABC is an isosceles right triangle with right angle B, and
DBE is an equilateral triangle. If the perimeter of DBE is 24, what is the
perimeter of ABC?
17.
A merry-go-round makes 8 revolutions per minute. Find the linear speed, in feet
per minute, of a horse 10 feet from the center. Leave your answer in terms of π
18.
The wheel of a machine rotates at the rate of 300 rpm (rotation per minute). If the
diameter of the wheel is 80 cm, what are the angular (in radian per second) and
linear speed (in cm per second) of a point on the wheel?
Evaluate or simplify:
19. tan x  27  tan    x   sec x sec x 
2

20. sin 34  cos56  3sin  3634
Trigonometry Review
Pre-Calc. for AP Prep.
Name: _________________
Date: _________________
Calculators
Solve for the sides or angles indicated. If there are no solutions, write “No Triangle”. If
there is more than one solution, give both. Any time a formula is used, show the
formula with values substituted. Round sides to the nearest hundredth and angles to
the nearest second.
1.
In ABC, A = 3215’, B is a right angle, and side b = 18 feet. Solve the
triangle.
2.
In LMN, m = 32.6 in, M = 279’17” and n = 41.3 in. Solve the triangle.
3.
Find the perimeter of the quadrilateral below.
20 ft
42
o
12 ft
110
o
10 ft
4.
A ship leaves port and sails northwest for 1 hour and then northeast for 2 hours
traveling at a constant rate of 300 km/hr.
a) How far is the ship from port?
b) How long will it take to return to port?
c) What angle should the ship turn at to return to port? (Give the bearing)
5.
A submarine dives at an angle of depression of 12 degrees. If it takes 6 minutes
to dive from the surface to a depth of 500 feet, how fast (in miles per hour) does it
travel along its sloping path downward?
6.
In the cube below, find AC in terms of the side length. Then find the acute angle
made by diagonals AC and BD. Round your answers to the nearest hundredth
and hundredth of a degree.
7.
A ship is due west of a lighthouse. A second ship is 12 miles south of the first
ship. The bearing from the second ship to the lighthouse is N 64 E. How far, to
the nearest tenth of a mile, is the first ship from the lighthouse?
8.
An object in simple harmonic motion has a frequency of ¼ oscillation per minute
and an amplitude of 8 feet. Using the sine function, write an equation for the
object’s motion.