- Mathematics - Precalculus
1. In triangle ABC, angle C is a right angle and BC = 11. If m(angle)B = 30 degrees, find AC.
A. 11sqrt3 / 3***
B. sqrt3 / 11
C. 11 / 2
D. 11sqrt3 / 2
2. Which of the following angles has a reference angle of pi / 9?
A. -56pi / 9
B. 16pi / 9
C. 29pi / 9
D. -37pi / 9***
3. Your town's public library is building a new wheelchair ramp to its entrance. By law, the maximum angle of incline for the ramp is 4.76 degrees. The ramp will have a vertical rise of 2 ft. What is the shortest horizontal distance that the ramp can span?
A. 15.3 ft.
B. 3.5 ft.
C. 24.0 ft.***
D. 9.5 ft.
4. Find the exact value of csc theta if cot there = -2 and the terminal side of theta lies in quadrant II.
A. csc theta = sqrt5***
B. csc theta = -sqrt5
C. csc theta = -sqrt5 / 2
D. csc theta = sqrt5 / 2
5. Which of the following has the same value as cos(5 theta / 6)? Select all that apply.
A. cos(pi / 6)***
B. cos(pi / 3)
C. sin(5pi / 3)***
D. cos(7pi / 6)
E. cos(11pi / 6)
6. Which trigonometric function is equivalent to f(x) = sin x?
A. f(x) = cos(-x + 3pi / 2)
B. f(x) = cos(x + pi / 2)***
C. f(x) = cos(-x + pi / 2)
D. f(x) = cos(-x + pi)
7 . Which trigonometric function requires a domain restriction of [-pi / 2, pi / 2] to make it invertable?
A. f(x) = sin x
B. f(x) = cos x
C. f(x) = tan x
D. f(x) = csc x***
E. f(x) = sec x
F. f(x) = cot x
8. What is the horizontal shift of the function y = 3sin(4x - pi)?
A. pi units to the right
B. pi / 2 units to the right
C. pi / 3 units to the right***
D. pi / 4 unit to the right
9. Which is the exact value of cos(-75 degrees)?
A. (sqrt6 + sqrt2) / 4
B. (sqrt6 - sqrt2) / 4***
C. (-sqrt6 + sqrt2) / 4
D. -((sqrt6 + sqrt2) / 4)
10. The sides of a triangle are 17 ft., 19 ft., and 15 ft. Find the measure of the angle opposite the longest side. Round your answer to the nearest degree.
A. 107 degrees
B. 73 degrees***
C. 59 degrees
D. 49 degrees
11. Find all solutions of the equation 2sin(2x)cos(x) - sin(2x) = 0 over the interval -pi / 2 < x < (or equal to) pi / 2
A. x = -pi/6, 0, pi/6, pi/2
B. x = -pi/3, -pi/4, pi/4, pi/3
C. x = -pi/4, -pi/6, pi/6, pi/4***
D. x = -pi/3, 0, pi/3, pi/2
12. Which polar coordinates represent the same point as the rectangular coordinate (1, -2)? Select all that apply.
A. (sqrt5, 63.4 degrees)
B. (sqrt5, 296.6 degrees)***
C. (-sqrt5, 116.6 degrees)
D. (-sqrt5, 153.4 degrees)
13. Which polar equation represents an ellipse?
A. r = 3 / (2 - 5 sin theta)
B. r = 2 / (2 - sin theta)***
C. r = 4 / (3 + 3 cos theta)
D. r = 5 / (3 + 4 cos theta)
14. Use DeMoivre's Theorem to find (4cis(pi / 18))^3
A. 32 + 32sqrt(3i)
B. 32sqrt(3) + 32i***
C. 6 + 6sqrt(31)
D. 6sqrt(3) + 6i
15. Which of the following points could be the initial point of vector v if it has a magnitude of 10 and the terminal point (-2, 4)?
A. (-0.2, 0.4)
B. (-8, -4)***
C. (-12, -6)
D. (1, 3)
16. Given vectors u = <-6, 4> and v = <7, 10>, determine if the vectors are orthogonal. If they are not orthogonal, find the angle between the two vectors.
A. The vectors are orthogonal
B. The vectors are not orthogonal. The angle between the two vectors is 91.3 degrees
C. The vectors are not orthogonal. The angle between the two vectors is 98.0 degrees
D. The vectors are not orthogonal. The angle between the two vectors is 80.6 degrees***
17. Use the graph to answer the question. Which statement matches the vector operation shown on the coordinate grid?
A. v + w = u for v = 6i + 5j, w = 2i - 4j, and u = 8i + j
B. v + w = u for v = 6i + 5j, w = 2i - 4j, and u = 4i + 9j
C. v + u = w for v = 6i + 5j, u = 8i + j, and w = 2i - 4j***
D. v + u = w for v = 6i + 5j, u = 8i + j, and w = 14i + 6j
18. Two forces act on an object. The first force has a magnitude of 400 newtons and acts at an angle of 30 degrees as measured from the horizontal. The second force has a magnitude of 280 newtons and acts at an angle of 135 degrees as measured from the horizontal. Determine the vector v that represents the resultant force.
A. v = (200 - 140sqrt(2))i + (200sqrt(3) + 140sqrt(2))j
B. v = (200 + 140sqrt(2))i + (200sqrt(3) + 140sqrt(2))j
C. v = (200sqrt(3) + 140sqrt(2))i + (200 + 140sqrt(2))j
D. v = (200sqrt(3) - 140sqrt(2))i + (200 + 140sqrt(2))j***
19. For v = 4i - 8j, find the unit vector u in the direction of v
A. u = 1/3i - 2/3j
B. u = i - j
C. u = sqrt3/3i - 2sqrt/3j
D. u = sqrt5/5i - 2sqrt(5)/5j***
20. Which of the following is a point on the plane curve defined by the parametric equations?
x = 4t
y = 12t^2 + 4t - 1
A. (4, 7)
B. (4, 207)
C. (-2, 4)
D. (-2, 0)***
21. Write the following parametric equations as a polar equation.
x = 4t
y = t^2
A. r = 4 cot (theta) csc (theta)***
B. r = 4 tan (theta) sec (theta)
C. r = 16 cot (theta) csc (theta)
D. r = 16 tan (theta) sec (theta)
22. A baseball player hits a ball at an angle of 56 degrees and at a height of 4.2 ft. If the ball's initial velocity after being hit is 154 ft./s and if no one catches the ball, when will it hit the ground? Remember that the acceleration due to gravity is 32 ft./s^2.
A. 8.01 seconds
B. 7.98 seconds
C. 5.43 seconds***
D. 5.38 seconds
23. Which set of parametric equations represents the function y = 4x^2 - 43x + 97?
A. x = t - 5
y = 4t^2 - 3t + 12
B. x = 2t
y = t^2 - 21t + 97
C. x = t + 5
y = 4t^2 - 3t - 18***
D. x = t + 3
y = 4t^2 - 19t + 5
24. Which is the polar form of the following parametric equations?
x = 4 sin^2 (theta)
y = 4 sin (theta) cos (theta)
A. r = 1/4 sin (theta) cos (theta)
B. r = 2
C. r = 16 sin^2 (theta)***
D. r = 4 sin theta
25. Find lim_x-->2 (x^2 + 3x - 10) / x-2
26. What is the equation of the line tangent to the function f(x) = 4x^2 + 5x at the point (-2, 6)?
A. y = -8x + 5
B. y = 8x +5
C. y = -11x + 16
D. y = -11x - 16***
Please tell me which ones are right. For ones that are wrong, it'd be great if I could get the answer :)
5. your probably meant: cos(5π/6) which is cos 150° = -.866..
so it is negative, ruling out A and B
C. sin(5pi / 3) ****
D. cos(7pi / 6) *****
8 y = 3sin(4x - pi) ---> y = 3sin(4(x - π/4) ) , so the shift is π/4
9 -10 ok
11. 2sin(2x)cos(x) - sin(2x) = 0
sin(2x)(2cosx - 1) = 0
sin(2x) = 0, 2x = 0, 2x = π, 2x = 2π
x = 0, π/2, ..
cosx = 1/2, x = ± π/3
so x = 0, π/2, ±π/3
12 - 15 ok
16. <-6,4)dot<7,10) = magnitude1 * magnitude2 * cos(theta)
-2 = √52√140cos theta
theta = 91.3°
I have only time for these right now, hope this helps.
You appear to be doing ok
turns out the questions are different on all tests. thanks anyway
Do y’all happen to have #17-26?
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