Name_________________________________________
I.
Block _____ Date _____________
Right Triangle Trigonometry – Remember in this section that we are
dealing with the ACUTE angles in a right triangle.
Find the exact value of the six trigonometric functions of the angle theta shown in the figure.
1.
2.
cos   ________
sec   ________
cos   ________
sec   ________
sin   ________
csc   ________
sin   ________
csc   ________
tan   ________
cot   ________
tan   ________
cot   ________
Sketch a right triangle corresponding to the trigonometric function of the acute angle theta. Find the
remaining five trigonometric functions of theta.
3. sin  
4. tan   3
5
6
cos   ________
sec   ________
cos   ________
sec   ________
sin   ________
csc   ________
sin   ________
csc   ________
tan   ________
cot   ________
tan   ________
cot   ________
Name_________________________________________
Block _____ Date _____________
Find the exact value of the variable(s).
5.
x = _________
6.
y = _________
x = _________
7.
y = _________
x = __________
r = ________
Draw a picture to represent the situation and then solve. Answer in a complete sentence. When
needed, round side lengths to the nearest tenth place and angle measures to the nearest whole
degree.
8. A 16-foot ladder is leaning against a building. If
the ladder forms a 38° angle with the ground,
determine how high the ladder reaches up the
building.
9. Michael is looking at the top of a mountain that is
2,050 feet high. If Michael is 6 feet tall (at eye level)
and he is looking up at a 10° angle to see the
mountain, how far is he from the mountain?
10. A fire department’s longest ladder is 110 feet.
The ladder reaches a height of 104 feet. At what
angle is the ladder placed against the ground?
11. A sonar operator on a ship detects a submarine
at a distance of 500 meters and an angle of
depression of 40°. How deep is the submarine?
Name_________________________________________
II.
Block _____ Date _____________
Unit Circle Trigonometry – You need to know the exact
value of the trig functions for the special angles we have
studied using the Unit Circle.
Evaluate the trig function for the given angle.
12. cos(135)
15. cos(135)
18. cos9
13. sec

16. cot(
14. sin(390)
2
15
)
4
19. sin(720)
17. csc
3
2
20. sec
5
3
Determine the value(s) of theta in degrees (0    360) and radians (0    2 ) .
12. sin  
3
2
15. cot   undefined
18. csc  
2 3
3
14. csc  2
13. tan   1
16. csc   
19. sec  2
2
2
17. cot   
20. sin   
3
3
1
2
Name_________________________________________
III.
Block _____ Date _____________
Trigonometric Functions of Any Angle
Draw the reference triangle using the given ordered pair.
21. (3, 2)
22. (-4, 4)
23. (-2, -6)
24. (5, -6)
25. (-3, 1)
26. (1, 7)
Determine in which quadrant the angle theta would lie.
27. sin   0 and cos  0
28. sec  0 and cot   0
29. csc  0 and tan   0
30. tan   0 and cos  0
31. sec  0 and sin   0
32. tan   0 and sec  0
Name_________________________________________
Block _____ Date _____________
The point given is on the terminal side of an angle in standard position. Determine the exact values of
the six trigonometric functions for the angle.
33. (3, -9)
34. (-5, 12)
cos   ________
sec   ________
cos   ________
sec   ________
sin   ________
csc   ________
sin   ________
csc   ________
tan   ________
cot   ________
tan   ________
cot   ________
Find the indicated trigonometric value for the angle described.
35. sec  2 and 0    
sec   _____
37. sin  
cot   0
3
and
5
tan   _____
36. cot   undefined and
csc   _____
38. cos   
and tan   0
3 10
10
sin   _____

2
 
3
2