Expert answer:Trigonometric Laws & Identities

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Trigonometric Laws & Identities
1. Given
with a = 19,
, and
, find b. Round the
sine value to the nearest thousandth and answer to the nearest hundredth.
A. 43
B. 19.45
C. 16.67
D. 11.38
2. Given
with a = 19,
, and
, find c.
Round the sine value to the nearest thousandth and the answer to
the nearest hundredth.
A. 43
B. 19.45
C. 16.67
D. 13.20
3. Given
with b = 19, c = 32, and
, find a. Round
the cosine value to the nearest thousandth and answer to the
nearest hundredth.
A. 20.33
B. 21.30
C. 22.43
D. 33.78
4. Given
with a = 22, b = 17, and c = 19, find
. Round the
cosine value to the nearest thousandth and answer to the nearest
whole degree.
A. 80 °
B. 75 °
C. 42 °
5. Given
with a = 9, b = 15, and
of distinct solutions.
A. none
B. 1
C. 2
6. Given
values for
with a = 9, c = 10, and
.
D. 19 °
, find the number
D. 3
, find both possible
A. 20°
B. 46°
C. 14°
D. no solution
7. Given
with a = 51.2, b = 33.7, and
value or possible values for
.
A. 46°
B. 53°
C. 39°
, determine the
D. no solution
8. Which of the following counterexamples proves that
is not a trigonometric identity? Select all that
apply.
A.0
B.
C.
D. 2π
9. Which of the following possible trigonometric identities can be
verified? Select all that apply.
A.
B.
C.
D.
10. Which of the following possible trigonometric identities can be
verified? Select all that apply.
A.
B.
C.
D.
11. Find the exact value for
A. 0
B.
C. 1
.
D. 2
12. Find the exact value for
A.
B.
.
C.
13. Find the exact value for
.
14. Solve the following equation for
Select all that apply.
A. 0
B.
C.
B.
C.
:
.
D.
15. Solve the following equation for
that apply.
A. 0
D.
:
. Select all
D. π
16. Find the area of a triangle with side lengths of 5, 7, and 10 units.
Round the answer to the nearest hundredth.
A. 16.25 units
B. 31.22 units
C. 25.14 units
D. 64.46 units
17. Find the area of a triangle with sides lengths 74.5, 50 and 50
units. Round the answer to the nearest hundredth.
18. Find the arc length of a circle if the central angle measures
and the radius measures 40 inches. Leave your answer in terms
of .
A. 5π inches
B. 10π inches C. 20π inches D. 40π inches
19. Find the arc length of a circle if the central angle measures 120°
and the radius measures 12 inches. Leave your answer in terms
of .
20. Find the area of a sector of a circle if the central angle measures
and the radius measures 20 inches. Leave your answer in
terms of .
A.
B.
C.
D.
21. Find the area of a sector of a circle if the central angle measures
and the radius measures 20 inches. Leave your answer in
terms of .
A.
B.
C.
D.
22. Find the angular displacement of 21.2 revolutions. Use
Round the answer to the nearest tenth. Show all work.
23. Determine the angular velocity in radians per second of 4.9
revolutions in 5 seconds. Use
. Round the answer to
the nearest tenth. Show all work.
.
24. Determine the linear velocity of an object with an angular
velocity of 8.1 radians per second at a distance of 10
centimeters from the center. Use
. Round the answer to
the nearest tenth.
A. 81 cm per second
C. 62 cm per second
B. 47 cm per second
D. 98 cm per second
25. If a wheel with a radius of 30 inches spins at a rate of 500
revolutions per minute, find the approximate linear velocity in
miles per hour. Use
.
A. 89 mph
B. 117 mph
C. 129 mph
D. 149 mph
…
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