Download 6.1+-+6.3+Practice+Test

6.1 – 6.3 Practice
Non-Calculator
Convert the following to degrees
𝜋
1. 5
2. -
𝜋
10
Convert the following to radians
3. 40˚
4. -160˚
Sketch the following angles in standard position
𝜋
5.
5
6. -160˚
Fill in quadrant I of the unit circle
7.
Degree
Radians
sin 
cos 
tan 
0
0
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30
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45
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60
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90
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180
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270
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2
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Calculator Section
Convert the degree minute second measure to degree decimal form (2 decimal places).
8. 138 15’ 29”
9. -254
30”
Convert to degree minute second form.
10. 172.463
11. –12.4762
Convert to degrees.
12. 1.25 (2 decimal places)
Convert to radians.
13. 42 15’ (2 decimal places)
Give a coterminal angles for each angle
14. –173
15. 5/6
Find the arc length (s = r ϴ)
16.
Find the area of the sector (A = ½ r2 ϴ)
17.
ϴ is 150˚
3 ft
18. Assuming that the earth is a sphere of radius 4,000 miles, what is the difference in
latitude of 2 cities, one of which is 400 miles due north of the other (answer in degree minute
second form)?
Hint, use s = r ϴ to find ϴ, convert to degrees, convert to DMS
19. What is the difference between angular velocity and speed?
The radius of a compact disc is 2.36 inches. It rotates at 360 revolutions per minute.
20. Find the angular velocity in radians per second.
21. Find the speed of a point (inches/second) on the circumference of the circle (2 decimal
places).
22. Use your circle to find the six functions of 7/6.
Sin t
(do not round, rationalize)
Csc t
Cos t
Sec t
Tan t
Cot t
23. Use a calculator to approximate the following to 4 decimal places.
a. Sin 12˚
b. Cos -83˚
c. Sec 15˚
𝜋
d. Sin 5
𝜋
e. Cot -10
24. Find sin , if  is in standard position and its terminal side passes through (7, -9).
25. In which quadrant is the sin positive and the cos negative?
26. Determine the quadrant in which  lies given tan  < 0, cos  > 0.
27. Given sin  = -1/5 and tan  < 0, find cos .
Use your trig ID’s to answer the following:
28. If sin ϴ = .25, what is the sin -ϴ?
29. If cos ϴ = .25, what is the cos -ϴ? .
30. If tan ϴ = -.25, what is the tan -ϴ?
31. If sin 30˚ = ½, what is the sin 390˚?
32. Sin2 18 + Cos2 18 =
33. (sin 18˚)(csc 18˚) = sin 18˚ •
1
sin 18˚
=
34. (Tan 108˚)(Cot 108˚) =
35. (Tan 200˚)(Cot 20˚) = (Tan 20˚)(Cot 20˚) =
Hint, change tan 200˚ to tan ?
Sin -330˚?