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1. What do you call the acute angle formed by the terminal side of an angle θ in standard position and the horizontal axis?
complementarysupplementary coterminalquadrantreference
2. In which quadrants is sin θ positive? (Select all that apply.)
Quadrant IQuadrant IIQuadrant IIIQuadrant IV
3. For which of the quadrant angles 0, π/2, π, and 3π/2 is the cos function equal to 0? (Select all that apply.)
0π/2π3π/2
4. Is the value of cos 165° equal to the value of cos 15°?
YesNo
5. Determine the exact values of the six trigonometric functions of the angle θ.
sin θ
=
cos θ
=
tan θ
=
csc θ
=
sec θ
=
cot θ
=
WebAssign Plot
6. Determine the exact values of the six trigonometric functions of the angle θ.
http://www.webassign.net/laratrmrp6/5-3-016.gif
sin θ
=
cos θ
=
tan θ
=
csc θ
=
sec θ
=
cot θ
=
7. Determine the exact values of the six trigonometric functions of the angle θ.
sin θ
=
cos θ
=
tan θ
=
csc θ
=
sec θ
=
cot θ
=
WebAssign Plot
8. The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle.
(−80, 18)
sin θ
=
cos θ
=
tan θ
=
csc θ
=
sec θ
=
cot θ
=
9. The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle.
(–7, –8)
sin(θ)
=
cos(θ)
=
tan(θ)
=
csc(θ)
=
sec(θ)
=
cot(θ)
=
10. The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle.
(5, −8)
sin(θ)
=
cos(θ)
=
tan(θ)
=
csc(θ)
=
sec(θ)
=
cot(θ)
=
11. State the quadrant in which θ lies.
sec θ > 0 and cot θ < 0
III IIIIV
12. State the quadrant in which θ lies.
tan θ > 0 and csc θ < 0
III IIIIV
13. Find the values of the six trigonometric functions of θ with the given constraint. (If an answer is undefined, enter UNDEFINED.)
Function Value
Constraint
csc θ = 6
cot θ < 0
sin θ
=
cos θ
=
tan θ
=
csc θ
=
sec θ
=
cot θ
=
14. Find the values of the six trigonometric functions of θ with the given constraint. (If an answer is undefined, enter UNDEFINED.)
Function Value
Constraint
tan θ is undefined.
π ≤ θ ≤ 2π
sin θ
=
cos θ
=
tan θ
=
csc θ
=
sec θ
=
cot θ
=
15. Evaluate the trigonometric function of the quadrant angle. (If an answer is undefined, enter UNDEFINED.)
sec π
16. Evaluate the trigonometric function of the quadrant angle. (If an answer is undefined, enter UNDEFINED.)
csc 0
17. Evaluate the trigonometric function of the quadrant angle. (If an answer is undefined, enter UNDEFINED.)
csc
3π
2
18. Evaluate the trigonometric function of the quadrant angle. (If an answer is undefined, enter UNDEFINED.)
csc
7π
2
19. Find the reference angle θ ' for the special angle θ.
θ = −295°
θ ' = ° Sketch θ in standard position and label θ '.
WebAssign Plot
WebAssign Plot
WebAssign Plot
WebAssign Plot
20. Find the reference angle θ ' for the special angle θ. (Round your answer to four decimal places.)
θ =
2π
3
θ ' = Sketch θ in standard position and label θ '.
WebAssign Plot
WebAssign Plot
WebAssign Plot
WebAssign Plot
21. Find the reference angle θ ' for the special angle θ. (Round your answer to four decimal places.)
θ = −
5π
6
θ ' = Sketch θ in standard position and label θ '.
WebAssign Plot
WebAssign Plot
WebAssign Plot
WebAssign Plot
22. Find the reference angle θ '.
θ = 326°
θ ' = ° Sketch θ in standard position and label θ '.
WebAssign Plot
WebAssign Plot
WebAssign Plot
WebAssign Plot
23. Evaluate the sine, cosine, and tangent of the angle without using a calculator. (If an answer is undefined, enter UNDEFINED.)
θ =
3π
4
sin θ
=
cos θ
=
tan θ
=
24. Evaluate the sine, cosine, and tangent of the angle without using a calculator.
– (7π)/6
sin(θ)
=
cos(θ)
=
tan(θ)
=
25. Find the indicated trigonometric value in the specified quadrant.
Function
Quadrant
Trigonometric Value
csc θ = –3
III
cot θ
cot θ =
26. Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle.
cos θ = −
5
9
, sin θ < 0
sin θ
=
tan θ
=
csc θ
=
sec θ
=
cot θ
=
27. Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle.
sec θ = −
5
4
, cot θ > 0
sin θ
=
cos θ
=
tan θ
=
csc θ
=
cot θ
=
28. Use the figure and a straightedge to approximate the value of each trigonometric function. Check your approximation using a graphing utility. To print an enlarged copy of the graph, go to the website www.mathgraphs.com. (Round your answers to one decimal place.)
http://www.webassign.net/larprecalcrmrp6/4-2-071.gif
(a) sin 1.25 (b) cos 2.75
29. Use the value of the trigonometric function to evaluate the indicated functions.
cos(t) = – 4/5
(a) cos(−t) (b) sec(−t)
30. Find the exact value of each function for the given angle for
f(θ) = sin θ
and
g(θ) = cos θ.
Do not use a calculator.
θ = 180°
(a)
(f + g)(θ)
(b)
(g − f)(θ)
(c)
[g(θ)]2
(d)
(fg)(θ)
(e)
f(2θ)
(f)
g(−θ)
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