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TRIGONOMETRY I

1. Find the sin, cos, tan, csc, sec, and cot of  .
7
Find x to the nearest hundredth.
2.
3.
15
x
36˚
6
4.
x
5.
11
x
19
16
28˚
52˚
x˚
8
Find x.
6. sinx = cos 53˚
8. sin (3x – 18) = cos (2x + 3)
7. sin (2x + 15) = cos x
Rewrite each angle in radians.
9. 62˚
Rewrite each angle in degrees.
6
12.
5
10. 245˚
13.
11. 1350˚
8
9
14. 7
15. A circle has a radius 8 inches and a central angle of 3 radians. What is the measure of
the intercepted arc?
16. A circle with radius 2.5 cm intercepts an arc of 12 cm. What is the measure of the
central angle?
Find the sin, cos, and tan of the angle that intercepts the point
17. (.8,.7)
18. (.2,.6)
Name the quadrant  lies in if
19. cos  < 0 and csc  > 0
21. csc  < 0 and cot  > 0
20. tan  < 0 and sec  > 0
22. sin  > 0 and sin  tan  < 0
SPECIAL RIGHT TRIANGLES
x
x
30˚
45˚
x
2
sin 45˚ =
2
2
cos 45˚ =
2
tan 45˚ = 1
x 3
sin 30˚ =
1
2
3
2
3
tan 30˚ =
3
cos 30˚ =
3
2
1
cos 60˚ =
2
sin 60˚ =
tan 60˚ =
3
0˚
QUADRANTAL ANGLES
(0,1)
180˚
270˚
90˚
(1,0)
sin 0˚ = 0
cos 0˚ = 1
tan 0˚ = 0
(-1,0)
sin 90˚ = 1
cos 90˚ = 0
tan 90˚ = undef
(0,-1)
sin 180˚ = 0
cos 180˚ = -1
tan 180˚ = 0
ANSWER KEY
7 85
cos  =
85
85
sec  =
7
6 85
85
85
csc  =
6
1. sin  =
2. x = 8.82
3. x = 12.99
4. x = 20.69
6. x = 37
7. x = 25
8. x = 21
9.
31
90
10.
49
36
12. 216˚
13. 160˚
15. 24 in
16. 4.8 radians
17. sin  = .7
cos  = .8
tan  = .875
19. II
360˚
11.
sin 270˚ = -1
sin 360˚ = 0
cos 270˚ = 0
cos 360˚ = 1
tan 270˚ = undef tan 360˚ = 0
6
7
7
cot  =
6
tan  =
5. x = 57.36˚
15
2
14. -1260˚
18. sin  = .6
cos  = .2
tan  = 3
20. IV
21. III
22. II
(1,0)