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4/25/2017
Semester Exam
Semester Exam
Sara Osborne is taking this assessment.
1. In 2. , is a right angle and BC = 7. If Which of the following angles has a reference angle of , find AC. (1 point)
?
(1 point)
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°. The ramp will have a vertical rise of 1.5 ft.
What is the shortest horizontal distance that the ramp can span?
(1 point)
11.5 ft.
2.6 ft.
7.1 ft.
18.0 ft.
4. Find the exact value of csc θ if and the terminal side of θ lies in quadrant II. (1 point)
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5. Semester Exam
Which of the following has the same value as 6. Which trigonometric function is equivalent to 7. ? Select all that apply.
(2 points)
? (1 point)
Which trigonometric function requires a domain restriction of to make it
(1 point)
invertable?
8. What is the horizontal shift of the function ? (1 point)
π units to the right
units to the right
units to the right
units to the right
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9. Which is the exact value of ? (1 point)
10. The sides of a triangle are 13 ft., 15 ft., and 11 ft. Find the measure of the angle opposite the
longest side. Round your answer to the nearest degree.
(1 point)
46°
58°
77°
103°
11. Find all solutions of the equation over the interval 12. Which polar coordinates represent the same point as the rectangular coordinate . (1 point)
? Select (2 points)
all that apply.
13. Which polar equation represents an ellipse? (1 point)
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14. Semester Exam
Use DeMoivre’s Theorem to find (1 point)
.
27i
9i
15. Which of the following points could be the initial point of vector v if it has a magnitude of 10 (1 point)
and the terminal point ?
16. Given vectors and , determine if the vectors are orthogonal. If they are
not orthogonal, find the angle between the two vectors.
(1 point)
The vectors are orthogonal.
The vectors are not orthogonal. The angle between the two vectors is 72.5°.
The vectors are not orthogonal. The angle between the two vectors is 101.3°.
The vectors are not orthogonal. The angle between the two vectors is 130.6°.
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Use the graph to answer the question.
17. Which statement matches the vector operation shown on the coordinate grid? (1 point)
v + w = u for v = 5i + 4j, , and u = 3i + 7j
v + w = u for v = 5i + 4j, , and u = 7i + j
v + u = w for v = 5i + 4j, u = 7i + j, and w = 12i + 5j
v + u = w for v = 5i + 4j, u = 7i + j, and 18. Two forces act on an object. The first force has a magnitude of 360 newtons and acts at an
(1 point)
angle of 30° as measured from the horizontal. The second force has a magnitude of 240
newtons and acts at an angle of 135° as measured from the horizontal. Determine the vector v
that represents the resultant force.
19. For , find unit vector u in the direction of v. (1 point)
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20. Which of the following is a point on the plane curve defined by the parametric equations? (1 point)
x = 3t 21. Write the following parametric equations as a polar equation. (1 point)
x = 4t r = 4 cot θ csc θ
r = 4 tan θ sec θ
r = 16 cot θ csc θ
r = 16 tan θ sec θ
22. A baseball player hits a ball at an angle of 56° 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 .
(1 point)
8.01 seconds
7.98 seconds
5.43 seconds
5.38 seconds
23. Which set of parametric equations represents the function ? (1 point)
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x = t + 5 x = t + 3 24. Which is a polar form of the following parametric equations? (1 point)
y = 7 cos θ sin θ
r = 7 cos θ
25. (1 point)
Find .
1
8
0
5
26. What is the equation of the line tangent to the function at the point ? (1 point)
y = 8x + 5
27. Determine if there are zero, one, or two triangles for the following: (4 points)
a = 10 m b = 12 m
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28. Semester Exam
What type of limaçon is graphed by the polar equation symmetry and horizontal and vertical intercepts.
? Identify the axis of
29. Note: Remember to show all of the steps that you use to solve the problem. Be sure to use the
text box where the question mark (?) first appears to show your mathematical work. You can
use the comments field to explain your work. Your teacher will review each step of your
response to ensure you receive proper credit for your answer. (4 points)
(4 points)
Write the composed trigonometric function in terms of x. Explain your steps
and/or show your work. Remember to rationalize the denominator if necessary.
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Select attachment
or drag and drop a file into this area ­ 20 MB limit
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Note: Remember to show all of the steps that you use to solve the problem. Be sure to use the (3 points)
text box where the question mark (?) first appears to show your mathematical work. You can
use the comments field to explain your work. Your teacher will review each step of your
response to ensure you receive proper credit for your answer. Verify the identity: Select attachment
or drag and drop a file into this area ­ 20 MB limit
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