Expert: Richard J. Raridon - 10/30/2011

Question
1.   Find the number of equivalent radians in exact value: 270°
  
2π/3
     
2/3π
  
3π/2
     
3/2π


2.   Find the number of equivalent radians in exact value: -180°
  
1/π
     
3/2π
  -π      2π


3.   Find the number of equivalent radians in exact value: 495°
  
4π/11
     
4/11π
  
11π/4
     
11/4π


4.   
Find the degree measure:   -p/2
  -270°      180°
  -90°      0°


5.   
Find the degree measure:    3π/4
  75°      45°
  215°      135°


6.   
Find the degree measure:    9π/4
  135°      405°
  445°      215°


7.   
Find the degree measure for the radian value:    -1/2
  
-90
π
     
-180
π
  
-π
2
     
-π
4


8.   Convert the given angle to the appropriate radian value: 300°
  5.24      4.76
  5.82      4.64


9.   Convert the given angle to the appropriate radian value: 255°
  1.05      8.97
  4.45      5.34


10.   Convert the radian measure to decimal degrees: -1.6
  -57.99°      -83.46°
  -74.68°      -91.7°


11.   Find the measure of the angle between 0 and 2π that is coterminal with a, where the degree measure of a = -60°.
  5.24       9.39
  3.42      2.34


12.   A merry-go-round 40 feet in diameter makes four revolutions every minute. What is the speed of the seat on the rim?
  88.57 ft/min      502.65 ft/min
  1,005.31 ft/min      54.36 ft/min


13.   Find the approximate sine, cosine, and tangent values for the radian measure: 1.4
  sine = 0.9854, cosine = 5.7979, tangent = 0.1700      sine = 0.9854,
cosine = 0.1700, tangent = 5.7979
  sine = 0.1700, cosine = 0.9854, tangent = 5.7979      sine = 5.7979, cosine = 0.1700, tangent = 0.9854


14.   Find the approximate sine, cosine, and tangent values for the radian measure: 0.7.
  sine = 0.6442, cosine = 0.8423. tangent = 0.7648       sine = 0.8423, cosine = 0.6442, tangent = 0.7648
  sine = 0.6442, cosine = 0.7648, tangent = 0.8423       sine = 0.8423, cosine = 0.7648, tangent = 0.6442


15.   
Find the exact values for the trig functions, with radian measure:    π
4
  sin = 1.414, cos = 1.414, tan = 0.7071, csc = 1, sec = 1, cot = 0.7071      sin = 0.7071, cos = 0.7071, tan = 1, csc = 1.414, sec = 1.414, cot = 1
  sin = 1, cos = 1, tan = 1.414, csc = 0.7071, sec = 0.7071, cot = 1.414       sin = 1, cos = 1, tan = 0.7071, csc = 1.414, sec = 1.414, cot = 0.7071


16.   
Find the exact values for the trig functions, with radian measure:    3π
4
  sin = -1, cos = -1, tan = 1.414, csc = 0.7071, sec = -0.7071, cot = -1.414       sin = 1.414, cos = -1.414, tan = -0.7071, csc = -1, sec = -1, cot = 0.7071
  sin = -1.414, cos = 1.414, tan = 0.7071, csc = -0.7071, sec = -1, cot = -1       sin = 0.7071, cos = -0.7071, tan = -1, csc = 1.414, sec = -1.414, cot = -1


17.   Find the exact value for the trig functions, with radian measure: π
  sin = 0, cos = -1, tan = 0, csc = undefined, sec = -1, cot = undefined       sin = -1, cos = 0, tan = undefined, csc = -1, sec = 0, cot = undefined
  sin = -1, cos = undefined, tan = 0, csc = undefined, sec = -1, cot = 0       sin = 0, cos = undefined, tan = -1, csc = undefined, sec = -1, cot = 0
18.   Find the number x if 0 ≤ x ≤ p/2 and x has the given function: csc x = 1.018
  0.999      0.0171
  1.23      1.38


19.   Find the exact radian value of x, where tan x = 1
  0.0548      0.9985
  
π/4
     0.4356


20.   
Express in degree measure:    -5π/6
  150      -150
  200      -225


21.   
Express in degree measure:    7π/4
  300      145
  315      225


22.   
Express in degree measure:    -3π/2
  270      180
  -180      -270


23.   Express in radian measure in terms of p: 140 degrees
  
7π/9
     
-3π/2
  
6π/5
     
-9π/7


24.   Express in radian measure in terms of p : 90 degrees
  
π/7
     
π/3
  
-π/5
     
π/2


25.   Express in radian measure in terms of p: -120 degrees
  
-2π/3
     
π/3
  
2π/2
     
2π/3


26.   Express the given radian measure in degree measure to the nearest degree: 2
  110      220
  115      105


27.   Express the given radian measure in degree measure to the nearest degree: -4
  -220      -115
  -229      -325


28.   Express the given radian measure in degree measure to the nearest degree: 2.3
  130      131
  132      133


29.   Express the given radian measure in degree measure to the nearest degree: -5.1
  -264      -292
  -324       -426


30.   Express the given radian measure in degree measure to the nearest degree: -1
  -61      -50
  -72      -57

Answer
1. 3pi/2
2. -pi
3. (11/4)pi
4. -90
5. 135
6. 405
7. -90/pi
8. 5.24
9. 4.45
10. -91.7
11. 5.24
12. 502.65
13. sine = 0.9854, cosine = 0.1700, tan = 5.7979
14. sine = p.6442, cosine = 0.7648, tan = 0.8423
15. sine = 0.7071, cosine = 0.7071, tan = 1, csc = 1.414, sec = 1.414, cot = 1
16. sine = 0.7071, cosine = -0.7071, tan = -1, csc = 1.414, sec = -1.414, cot = -1
17. sine = 0, cosine = -1, tan = 0, csc = undef, sec = -1, cot = undef
18. 1.38
19. pi/4
20. -150
21. 315
22. -270
23. 7pi/9
24. pi/2
25. -2pi/3
26. 115
27. -229
28. 132
29. -292
30. -57