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Math Analysis Homework
5.1 – 5.3
Please answer the following questions. Show your work and write your answer in the blanks.
Determine the reference angle, θ′, for the following angle measures of θ from standard position.
1. 285°
4. 320°
7
4
2.
3.
8
3
θ′ = ________
θ′ = ________
θ′ = ________
θ′ = ________
5. Determine the exact values of the six trigonometric functions of an angle of 330°.
cos θ = _____
sin θ = _____
tan θ = _____
6. Determine each value to four decimal places.
a) cos 153°
2
7
b) tan
c) sec
5
3
sec θ = _____
csc θ = _____
d) sec 18°
e) sin(-16.8°)
cot θ = _____
f) csc
3
7
Determine the value of θ, where 0° < θ < 360°, to the nearest tenth of a degree.
7. sin θ = -0.5772
8. tan θ = -0.3309
7)_________________________
8)_________________________
Determine the value of θ, where 0 < θ < 2π, to the nearest hundredth of a radian.
9. csc θ = -1.8391
10. cos θ = -0.4721
11. sec θ = 7.2986
9)________________________
10)_______________________
11)_______________________
12. cos2 θ + sin2 θ = _____
In which quadrant does the terminal side of θ lie from standard position?
13. tan θ < 0 and sin θ > 0
14. 0 < θ < π and cot > 0
15. sec   3 and csc   
16. sin    72 and sec θ < 0
17. tan    54 and  2    2
18. cos θ > 0 and csc θ < 0
6
2
Find the values for x, y, and r for each of the following situations.
19. cos   117 & θ in quadrant II 20. sin   85 and 0 < θ < 2
21. tan    94 and sin θ > 0
x = ____
x = ____
x = ____
y = ____
y = ____
y = ____
r = ____
22. csc   127 and cos θ > 0
r = ____
23. cot  
x = ____
x = ____
x = ____
y = ____
y = ____
y = ____
r = ____
r = ____
r = ____
5
6
and csc θ < 0
r = ____
24. sec   157 and - 2 < θ < 0
Given the following information, find the exact value of the six trig functions.
25. (-3, -3) is a point on the terminal side of θ.
26. (  53 , 2) is a point on the terminal side of θ.
sin θ = ______ cos θ = ______ tan θ = ______
sin θ = ______ cos θ = ______ tan θ = ______
csc θ = ______ sec θ = ______ cot θ = ______
27. The terminal side of θ intersects the unit
 3 2 10 
.
circle at   ,
7 
 7
csc θ = ______ sec θ = ______ cot θ = ______
sin θ = ______ cos θ = ______ tan θ = ______
sin θ = ______ cos θ = ______ tan θ = ______
csc θ = ______ sec θ = ______ cot θ = ______
csc θ = ______ sec θ = ______ cot θ = ______
7
30.  
3
29. cos  
3
and tan θ < 0
2
sin θ = ______ cos θ = ______ tan θ = ______
csc θ = ______ sec θ = ______ cot θ = ______
2 14
5
28. sin θ =  , and cos θ =
.
9
9
sin θ = ______ cos θ = ______ tan θ = ______
csc θ = ______ sec θ = ______ cot θ = ______