Expert: Richard J. Raridon - 7/29/2010

Question
1. Sketch the angle in standard position, indicating its rotation by a curved arrow. Choose the quadrant where the angle is located. Angle: 40°  III  I
IV  II  

2. Sketch the angle in standard position, indicating its rotation by a curved arrow. Choose the quadrant where the angle is located. Angle: 240°  III  I
IV  II

3. Sketch the angle in standard position, indicating its rotation by a curved arrow. Choose the quadrant where the angle is located. Angle: -90°  IV  II
Quadrantal angle  I

4. Sketch the angle in standard position, indicating its rotation by a curved arrow. Choose the quadrant where the angle is located. Angle: 1080°  Quadrantal angle  IV
II  I  

5. Sketch the angle in standard position, indicating its rotation by a curved arrow. Choose the quadrant where the angle is located. Angle: 750°  II  III
IV  I  

6. Sketch the following in standard position and find the measure: 3/8 of a counterclockwise revolution  135°   45°
165°  85°

7. Sketch the following in standard position and find the measure: 1/6 of a clockwise revolution  -120°  120°
60°  -60°

8. Sketch the following in standard position and find the measure: 2 and 1/3 counterclockwise revolutions  720°  540°
840°  620°

9. Determine the correct formula for the measures of all angles coterminal with the angle: 140°  140° + (360° + n)  140° + n(360°)
360° + n(180°)  360° + (180° + n)

10. Determine the correct formula for the measures of all angles coterminal with the angle: -210°  360° - (210°)  -210° + n(180°)  
-210° + n(360°)  360° + (210°)  

11. Determine the correct formula for the measures of all angles coterminal with the angle: -3605°  3605° - n(180°)  -3605° + n(360°)
-5° + n(180°)  3605° + n(360°)

12. Choose the correct decimal degrees for: 47° 36'  47.36°  47.5°  
47.6°  47.74°  

13. Choose the correct decimal degrees for: 33° 15'  33.25°  33.15°
33.30°  33.20°

14. Choose the correct decimal degrees for: 0° 42' 30"  0.42°   0.30°  
0.71°  0.84°  

15. Choose the correct degrees and minutes for: 63.6°  63° 36'  63° 60'
63° 6'  63° 12'

16. Choose the correct degrees and minutes for: 18.27°  18° 16'  18° 27'  
18° 24' 12"  18° 16' 12"

17. Choose the correct degrees and minutes for: 58.83°  58° 83'  58° 48' 49"
58° 49' 48"  58° 40' 83"

18. Choose the measure of the angle whose terminal side in standard position passes through: (-4, 4)  θ = 135°  θ = 45°
θ = 55°  θ = 125°

19. Write the 6 trig values in exact form for the acute angle formed by the line passing through the point: P(3, 4) sin θ = 5/4, cos θ = 3/5, tan θ = 4/3, csc θ = 4/5, sec θ = 5/3, cot θ = 3/4  sin θ = 4/5, cos θ = 3/5, tan θ = 4/3, csc θ = 5/4, sec θ = 5/3, cot θ = 3/4
sin θ = 5/4, cos θ = 5/3, tan θ = 4/3, csc θ = 5/4, sec θ = 3/5, cot θ = 3/4   sin θ = 4/5, cos θ = 5/3, tan θ = 3/4, csc θ = 4/5, sec θ = 3/5, cot θ = 4/3

20. Solve: sin θ = cos 50°  
θ = 140°  θ = 64°
θ = 40°  θ = 120°  

21. Solve: tan θ = cot 17°  
θ = 1070°   θ = 73°
θ = 67°  θ = 1120°

22. Choose the correct measure of the reference angle a where θ = -112°  
112°  68°
72°  94°

23. Choose the correct measure of the reference angle a where θ = -611°
109°  83°
63°  71°  

24. Choose the correct measure of the reference angle a where θ = 312° 50'
472° 50'  48° 10'  
380° 20'  47° 10'

25. Express the following as a function of an acute angle: sec (-106°)  
sec 106°   sec 74°
-sec 74°  -sec 106  

26. Express the following as a function of an acute angle: sin (-46.6°)  
-sin 133.4°  -sin 46.6°
sin 46.6°  sin 133.4°

27. Express the following as a function of an acute angle: sin 324° 30'  
sin 143° 30'  sin 35° 70'
-sin 35° 30'  -sin 143° 30'

28. Choose the quadrant in which the angle is found: cos θ = -3/5, sin θ > 0  
II   III
IV  I

29. Choose the quadrant in which the angle is found: sec θ = 13/5, sin θ < 0  
II  I
IV  III

30. Choose all angles θ, where 0° ≤ θ < 360° and sin θ = 1  θ = 180°   θ = 90°  
θ = 45°  θ = 270°

Answer
I usually don't answer this many questions at one time but many of these were simple enough that I didn't have to use a calculator
1. I
2. III
3. IV
4. I
5. I
6. 135
7. -60
8. 840
12. 47.6
13. 33.25
14. 0.71
15. 63 deg 36'
16. 18 deg 16' 12"
17. 58 deg 49' 48"
18. 135
20. 40
21. 73
22. 248
23. 109
24. 47 deg 10'
25. sec 106
26. -sin(46.6)
27. -sin(35 deg 30')
28. II
29. IV
30. 90