Expert answer:Trigonomic Functions
Answer & Explanation:I need help with these trigonomic functions. See attached document.Trigonomic functions
trigonomic_functions.doc
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1. Which of the following relations is a function?
A. {(-6, 4), (-6, 2), (2, 9), (1, 4)}
C. {(1, 2), (4, -1), (1, 2), (-3, 4)}
B. {(8, 2), (9, -2), (7, 0), (-3, 6)}
D. {(8, -2), (-4, 3), (8, 4), (-2, 3)}
2. Find the slope of the line through the points (4, 4) and (-1, 5).
A. m = 5
B. m = -5
C.
D.
3. What is the y-intercept of the line
A. 3
B. -3
C.
?
D.
4. Find the slope of the line through the points (-1, 7) and (3, 7).
A. m = -4
B. m = 4
C. The slope is zero
5. Write the equation of the line with m =
A.
B.
C.
D.
and b =
D. The slope is undefined
.
6. Explain why horizontal lines have a slope of zero.
7. Explain how a graph passes the vertical line test.
8. Explain why there are restrictions on the domain for the function,
9. The following graph represents ________________.
.
A. a relation
B. a function
C. an equation
D. an element
10. What is the domain of the following function?
A. {1, 2, 3, 4}
B. {2, 3, 4, 5}
C. {1, 2, 3, 5}
D. {4, 5, 6, 7}
11. What is the equation that passes through the points (8, 4) and (4, 0)?
A.
B.
C.
12. What is the domain of
A. x = 22
?
B.
C.
D.
13. What is the domain of
A.
14. Find
A. 13
D.
?
B.
C.
for
B. 2x – 5
D.
and
C.
.
D.
15. Find g(f(x)) if f(x) =
and g(x) =
A. -5x + 4 B. -5x – 2
C. -4x – 2
D. -4x + 4
16. What is the trigonometric ratio for
A.
B.
C.
B.
C.
?
D.
17. What is the trigonometric ratio for
A.
.
?
D.
18. Find the length of b, which is the side opposite angle B. Round your answer to the
nearest tenth.
A. 6.3 units
B. 12.7 units
C. 9.4 units
D. 13.6 units
19. Find . Round your answer to the nearest whole degree.
A. 37°
B. 53°
C. 64°
D. 90°
20. A ladder is leaning up against a 70-foot wall at an angle of elevation of 38°. How far is
the foot of the ladder from the wall? Round your answer to the nearest tenth of a foot.
A. 22.2 ft
B. 38.9 ft
C. 54.7 ft
D. 89.6 ft
21. Determine the quadrant in which the terminal side of a 237° angle in standard
position lies.
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
22. Convert 315° to radians.
A.
B.
C.
D.
23. Which of the following angles is coterminal with 230°?
A. 30°
B. 130°
C. -60°
D. -130°
24. Which of the following angles is a quadrant angle?
A. 45°
B. 145°
C. 180°
25. Find the exact value for
D. 500°
.
26. Determine the angular velocity in radians per second of 4.3 revolutions in 5 seconds.
Use π = 3.14. Round the answer to the nearest tenth. Show all work.
27. Explain the meaning of SOH of the mnemonic device SOH-CAH-TOA.
28. Find the tangent of 135°.
A. 1
B.
D. -1
C.
29. Find the area of a triangle with sides lengths 17, 18, and 21.4 units. Round the answer
to the nearest hundredth.
30. What is the period of the function
A. 10π
B. 5π
C. 2π
?
D.
31. What is the range of the function
A.
B.
?
C.
D.
32. What is the period of the function represented by the following graph?
A. 4π
B. 2π
C. π
D.
33. Which parent graph represents the reciprocal of the sine function?
A.
B.
C.
D.
34. Explain how the transformations of the functions
differ.
and
35. Which of the following graphs represents a vertical shift down 1 of the parent graph of
?
A.
B.
C.
D.
36. Write the equation of the sine function with amplitude of 8.5, standard period, phase
shift of 90°, and a vertical shift of 12.
37. Which graph does the table of values approximately represent?
x
y
-2
-3
-1
-2
0
0
1
2
2
3
A.
B.
C.
D.
38. The temperature in your house is controlled by a thermostat. The temperatures will
vary according to the sinusoidal function:
, where f(x)
represents the temperature in degrees Celsius (°C) and x is hours since midnight. What is
the temperature of your house at midnight?
A. 7° C
B. 16° C
C. 22° C
D. 31° C
39. The population of rabbits varies with respect to time, in days, as a sinusoidal function.
The graph below represents the variation in population. From the graph determine the
amplitude.
A. 10
B. 15
C. 17
D. 28
40. Explain the difference between a vector and scalar.
41. Perform the scalar multiplication for the following:
A.
B. (3, 8)
42. Given the vectors
and
43. Given
A. (1, 0)
C. (11, 6)
.
D. (28, -7)
and
, explain the difference between
.
and
B.(-7, 4)
, find
C.(-12, -4)
.
D. (-1, -4)
44. Given
with a = 24,
, and
, find b. Round the sine
value to the nearest thousandth and the answer to the nearest hundredth.
A. 28.92
B. 21.64
C. 13.07
D. 13.42
45. Given
with b = 5, c = 26, and
, find a. Round the cosine value to
the nearest thousandth and answer to the nearest hundredth.
A. 17.49
B. 25.51
C. 25.93
D. 29.09
46. Given
with a = 45, b = 5, and c = 45, find
. Round the cosine value to the
nearest thousandth and answer to the nearest hundredth.
A. 138°
B. 16°
47. Given
for
with a = 10, b = 16, and
A. 53°, 127°
B. 53°, 133
C. 14°
D. 6°
, determine both possible values
C. 64°, 127
D. no solution
48. Find the area of a sector of a circle if the central angle measures
measures 6 inches. Leave your answer in terms of .
A.
B.
C.
D.
49. Verify the following trigonometric identity:
50. Find the exact value for
A.
B.
.
C.
D.
and the radius
…
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