Download College Trigonometry Final Exam Name: (1

College Trigonometry Final Exam
Name:___________________________
(1-12 are worth 3pts each, 13-28 are worth 4pts each)
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Write an equation of a parabola with a vertex at the origin and a focus at (0, –2).
a.
c.
b.
____
d.
2. Find the measure of the angle below.
y
15

x
a. 255º
b. 90º
c. 105º
____
3. In which quadrant does the terminal side of a –322º angle lie?
a. second quadrant
c. third quadrant
b. fourth quadrant
d. first quadrant
____
4. Find the exact value of cos 300º and sin 300º.
a.
c.
b.
____
d. 195º
d.
5. A particular sound wave can be graphed using the function
. Find the amplitude and period of the
function.
a.
c.
2
5
amplitude = , period = 7
amplitude = , period = –7
5
2
b.
d.
2
5
amplitude = 7, period = 
amplitude = –7, period =
5
2
Sketch the angle in standard position.
____
6.
320º
a.
c.
y
y

320

320
x
b.
d.
y
x
y

320

320
x
x
Simplify the trigonometric expression.
____
7.
a.
b.
Solve the equation for 0 
____
c.
d.
< 2. Write your answer as a multiple of , if possible.
8.
a.
c.
b.
d.
Write a cosine function for the graph.
____
9.
y
4
2
O

2

–2
–4
a.
c.
b.
d.
____ 10. Use the Law of Sines. Find
to the nearest tenth.
C
56
61°
B
64
a. 91.7
b. 49.9
A
c. 130.1
d. 88.3
____ 11. Use the Law of Cosines. Find
to the nearest tenth of a degree.
C
2
3
B
4
a. 52.8
b. 46.6
A
c. 62.7
d. 29.0
c.
d.
Find the exact value of the expression.
____ 12. cos 165°
a.
b.
Short Answer
13. Find the foci of the ellipse with the equation
.
14. Graph
.
. Graph the ellipse
15. Identify the focus and the directrix of the graph of
.
Write the measure in radians. Express the answer in terms of .
16. –290º
Write the measure in degrees.
17. –
radians
18. Suppose
. Find
.
19. The line of sight from a small boat to the light at the top of a 40-foot lighthouse built on a cliff 20 feet above
the water makes a 27° angle with the water. To the nearest foot, how far is the boat from the cliff?
40
ft
27 
Drawing is not to scale.
20 ft
Find the length x. Round to the nearest tenth.
20.
x
35
41 °
21. What is the simplified form of sin(x + )?
22. To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit
4 feet tall, measures the angle of elevation to the top of the pole to be 44 . To the nearest foot, what is the
height of the pole?
.
23. Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts
a shadow 14 yards long. Round to the nearest degree.
24. Perform the indicated operation, where u = < 3,-1 > and v = <- 6,7>.
a.
b.
c.
d.
v•u
2u - 3v
||u|| + ||v||
Find the angle between u and v. (To the nearest degree.)
Simplify, write the complex number in a + bi form
25. (2 + 3i) + (-7 + 2i)
26. (6 + 11i)(8 – 2i)
Write the complex number in trigonometric form.
27. z =4 + 2i
Find the indicated roots. Write your answer in trigonometric form.
28. The three cube roots of 3 + 2i