Advanced Math/Trigonometry Chapter 3 Part I Review
PA Standards: 2.3; 2.10
Anchors: A2; B1
1. Convert each into revolutions and radians.
a. 320
c. -260
2. Convert each into revolutions and degrees.
9
a.
8
c.
4
9
3. Convert each into degrees and radians.
5
a. revolutions
3
c. 4
1
revolutions
4
4. Express each in degree-minute-seconds.
a. 33.47
c. -56.25
b. 390
d. 480
b. -
17
18
d.
8
3
b.
5
revolutions
8
d.
3
revolutions
5
b. 20.11
d. -10.33
5. Express each in decimal degrees.
a. 6730′56″
c. 165′44″
b. -510′24″
d. -3810′25″
6. Determine the arc length of a circle of diameter 49 m that is intercepted by a central angle of 45.
7. Determine the arc length of a circle of diameter 23.8 m that is intercepted by a central angle of
155.
8. Determine the arc length of a circle of diameter 12 m that is intercepted by a central angle of 90.
9. Find the area of the sector with a central angle of

and a radius of 10 in.
8
10. Find the area of the sector with a central angle of
2
and a radius of 7 cm.
3
11. Find the area of the sector with a central angle of

and a radius of 12 cm.
5
12. Given that a point on a wheel turns at 150 rpm, find the angular velocity in radians per second.
13. Given that a point on a wheel turns at 720 rpm, find the angular velocity in radians per second.
14. Given that a point on a wheel turns at 350 rpm, find the angular velocity in radians per second.
15. Find the linear velocity of a point on a wheel 15 cm from the center that moves through an angle
of 30 per second.
16. Find the linear velocity of a point on a wheel 12 cm from the center that moves through an angle
of 150 per second.
17. Find the linear velocity of a point on a wheel 16 cm from the center that moves through an angle
of 135 per second.
18. Name the three pairs of trigonometric cofunctions.
19. Name the three pairs of trigonometric reciprocal functions.
20. Given that sin  =
1
and is in QII, find the exact value of cos .
6
21. Given that sin  = -
3
and is in QIII, find the exact value of cos .
4
22. Given that sin  = -
13
and is in QIV, find the exact value of cos .
20
23. The terminal side of an angle in standard position passes through (-3, 4). Draw a reference
triangle and name the exact values of the six trigonometric functions.
y
x
sin  = _______
csc  = _______
cos  = _______
sec  = _______
tan  = _______
cot  = _______
24. The terminal side of an angle in standard position passes through (-7, -24). Draw a reference
triangle and name the exact values of the six trigonometric functions.
y
x
sin  = _______
csc  = _______
cos  = _______
sec  = _______
tan  = _______
cot  = _______
25. The terminal side of an angle in standard position passes through (12, -5). Draw a reference
triangle and name the exact values of the six trigonometric functions.
y
x
26. If cos  =
2
, then sec  = _______.
3
27. If sin  =-0.7, then csc  = _______.
sin  = _______
csc  = _______
cos  = _______
sec  = _______
tan  = _______
cot  = _______
28. Use your calculator to evaluate each. Round your answers to four decimal places.
a. sin 138 = ___________
b. sec 320 = __________
c. tan 3.6 = ____________
d. sin 15 = ___________
e. cos 195 = __________
f. csc 340= ____________
g. cot 7.2 = ___________
h. cos (-72) = __________ i. tan (-75)= ____________
j. sin
3
= ___________
5
k. sec
7
= __________
5
l. tan 48= ____________
m. cot 210 = ___________
n. cos 1.4 = __________
o. csc 2.6 = ____________
p. cot 218 = ___________
q. cos 5.12 = __________
r. csc
s. sin 1216′2″ = ___________
t. sec (-23) = __________ u. tan 5234′32″ = ____________
v. sin 6.9 = ___________
w. cos 953′7″ = ________ x. csc 35.67= ____________
9
= ____________
7
29. Draw the reference triangles and name two angles for each. 0   < 360.
a. sin  = -0.6428
b. cos  = -0.8192
y
y
x
c. tan  = -0.3639
x
d. cot  = 0.1763
y
y
x
e. sec  = 3.8637
x
f. csc  = 1.3054
y
y
x
x
30. Draw the reference triangles and name two angles for each. 0   < 2.
a. sin  = 0.5985
b. cos  = 0.8855
y
y
x
c. tan  = 1.7778
x
d. cot  = 0.3888
y
y
x
e. sec  = 1.3667
x
f. csc  = 2.9163
y
y
x
x