Precalculus homework
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162test2.pdf
162 Test 2 Name: Warm up questions 2 points each.
1. The domain of sine is and the range is .
2. The domain of cosine is and the range is .
3. What numbers are excluded from the domain of tangent?
4. The range if tangent is .
5. The domain of sin−1(x) is and the range is .
6. The domain of tan−1(x) is and the range is .
7. If sin(α) = −.3 then sin(−α) = .
8. If cos(β) = −.7 then cos(−β) = .
9. Graph y = sin(x) on the left and y = cos(x) on the right.
x
y = sin(x)
x
y = cos(x)
10. sin(0) = , cos(0) = tan(0) = .
11. sin ( 7π 6
) = , cos
( 7π 6
) = , tan
( 7π 6
) =
12. sin ( −π
4
) = , cos
( −π
4
) = , tan
( −π
4
) =
13. sin−1 (√
3 2
) = , cos−1
(√ 3 2
) =
1
Questions worth 4 points each.
14. Find all the trigonmetric functions of α.
9
4
α
(a) sin(α) =
(b) cos(α) =
(c) tan(α) =
(d) sec(α) =
(e) csc(α) =
(f) cot(α) =
15. Using your answer above, find sin(tan−1( 4 9 ))
16. More generally, find sin(tan−1(x))
17. Let f(x) = −2 sin (π
2 x )
. The period is and the amplitude is .
2
18. Graph f(x) = −2 sin (π
2 x )
clearly labeling the x and y axes.
x
y = −2 sin (π
2 x )
19. Solve the triange with A = 35◦,C = 95◦,a = 10
i B =
ii b =
iii c =
20. Solve the triangle with a = 7,b = 8,c = 9
i A =
ii B =
iii C =
3
21. For the function below, find the amplitude and the period.
(a) Period:
(b) Amplitude:
22. Using your answer above, give a good guess as to what function was graphed.
23. (Extra Credit) For the function below, find the amplitude and the period.
(a) Period:
(b) Amplitude:
24. What function was graphed?
4
