Advanced Math/Trigonometry Chapter 3 Part I Review
Advanced Math/Trigonometry Chapter 3 Part I Review
PA Standards: 2.3; 2.10Anchors: A2; B1
1. Convert each into revolutions and radians.
a. 320b. 390
c. -260d. 480
2. Convert each into revolutions and degrees.
a. b. -
c. d.
3. Convert each into degrees and radians.
a. revolutionsb. revolutions
c. revolutionsd. revolutions
4. Express each in degree-minute-seconds.
a. 33.47b. 20.11
c. -56.25d. -10.33
5. Express each in decimal degrees.
a. 6730′56″b. -510′24″
c. 165′44″d. -3810′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.
10. Find the area of the sector with a central angle of and a radius of 7 cm.
11. Find the area of the sector with a central angle of and a radius of 12 cm.
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 = and is in QII, find the exact value of cos .
21. Given that sin = - and is in QIII, find the exact value of cos .
22. Given that sin = - and is in QIV, find the exact value of cos .
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.
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.
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.
26. If cos = , then sec = ______.
27. If sin =-0.7, then csc = ______.
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 = ______k. sec = ______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 1216′2″ = ______t. sec (-23) = ______u. tan 5234′32″ = ______
v. sin 6.9 = ______w. cos 953′7″ = ______x. csc 35.67= ______
29. Draw the reference triangles and name two angles for each. 0 < 360.
a. sin = -0.6428b. cos = -0.8192
c. tan = -0.3639d. cot = 0.1763
e. sec = 3.8637f. csc = 1.3054
30. Draw the reference triangles and name two angles for each. 0 < 2.
a. sin = 0.5985b. cos = 0.8855
c. tan = 1.7778d. cot = 0.3888
e. sec = 1.3667f. csc = 2.9163