Precalculus
bdadio
precalculus6.docx1. 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.
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sin θ |
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cos θ |
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tan θ |
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csc θ |
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sec θ |
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cot θ |
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6. Determine the exact values of the six trigonometric functions of the angle θ.
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sin θ |
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cos θ |
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tan θ |
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csc θ |
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sec θ |
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cot θ |
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7. Determine the exact values of the six trigonometric functions of the angle θ.
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sin θ |
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cos θ |
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tan θ |
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csc θ |
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sec θ |
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cot θ |
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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)
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sin θ |
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cos θ |
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tan θ |
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csc θ |
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sec θ |
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cot θ |
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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)
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sin(θ) |
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cos(θ) |
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tan(θ) |
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csc(θ) |
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sec(θ) |
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cot(θ) |
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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)
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sin(θ) |
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cos(θ) |
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tan(θ) |
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csc(θ) |
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sec(θ) |
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cot(θ) |
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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.)
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Function Value |
Constraint |
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csc θ = 6 |
cot θ < 0 |
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sin θ |
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cos θ |
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tan θ |
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csc θ |
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sec θ |
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cot θ |
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14. Find the values of the six trigonometric functions of θ with the given constraint. (If an answer is undefined, enter UNDEFINED.)
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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
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3π |
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2 |
18. Evaluate the trigonometric function of the quadrant angle. (If an answer is undefined, enter UNDEFINED.)
csc
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7π |
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2 |
19. Find the reference angle θ ' for the special angle θ.
θ = −295°
θ ' = ° Sketch θ in standard position and label θ '.
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20. Find the reference angle θ ' for the special angle θ. (Round your answer to four decimal places.)
θ =
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2π |
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3 |
θ ' = Sketch θ in standard position and label θ '.
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21. Find the reference angle θ ' for the special angle θ. (Round your answer to four decimal places.)
θ = −
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5π |
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6 |
θ ' = Sketch θ in standard position and label θ '.
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22. Find the reference angle θ '.
θ = 326°
θ ' = ° Sketch θ in standard position and label θ '.
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23. Evaluate the sine, cosine, and tangent of the angle without using a calculator. (If an answer is undefined, enter UNDEFINED.)
θ =
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3π |
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4 |
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sin θ |
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cos θ |
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tan θ |
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24. Evaluate the sine, cosine, and tangent of the angle without using a calculator.
– (7π)/6
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sin(θ) |
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cos(θ) |
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tan(θ) |
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25. Find the indicated trigonometric value in the specified quadrant.
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Function |
Quadrant |
Trigonometric Value |
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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 = −
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5 |
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9 |
, sin θ < 0
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sin θ |
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tan θ |
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csc θ |
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sec θ |
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cot θ |
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27. Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle.
sec θ = −
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5 |
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4 |
, cot θ > 0
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sin θ |
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cos θ |
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tan θ |
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csc θ |
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cot θ |
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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.)
(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)
