Download Analysis Final Review B

Analysis Final Exam Review B
1. Sketch a positive angle with its terminal side in
Quadrant IV.
5.
Sketch a right triangle corresponding to the
trigonometric function of the acute angle Use the
Pythagorean Theorem to determine the third side
and then find the indicated trigonometric function
of
Express the angle in degree measure.
6. If
2.
Use a calculator to evaluate the function. Round
your answer to four decimal places. (Be sure the
calculator is in the correct angle mode.)
Convert the measure from degrees to radians.
Round to three decimal places.
3. 192176
find
7.
Find one positive angle and one negative angle that
are coterminal with the given angle.
Use the fundamental trigonometric identities to
determine a simplified form of the expression.
4. –
8.
Find the exact value of the six trigonometric
functions of the
given in the figure. (Use
the Pythagorean Theorem to find the third side of
the triangle.)
9. A photographer points a camera at a window in a nearby building forming an angle of
with the camera
platform. If the camera is 54 meters from the building, how high above the platform is the window? Round to two
decimal places.
The point given is on the terminal side of an angle
in standard position. Find the cotangent, the secant,
and the cosecant of the angle.
10.
Find the exact value of the function.
11.
Find the indicated trigonometric value in the
specified quadrant.
12.
is in Quadrant II and
Find
Rewrite the indicated trigonometric function in
terms of the angle's reference angle. Use the same
function.
13.
Sketch a graph of the function that has the given
amplitude and period.
17. Cosine function,
,
List the key points on the graph of the function.
14.
on the interval
Sketch the graph of the function.
15.
on the interval
Sketch the graph of the function and write
equations for 2 consecutive asymptotes.
18.
Sketch the graph of the function.
16.
, on the interval
Sketch the graph of the function and write
equations for 2 consecutive asymptotes.
23.
19.
Find all solutions of the equation in the interval
24.
Find all solutions of the equation in the interval
25.
Solve the equation.
26.
Sketch the graph of the function. Include any
asymptotes.
20.
Find the exact value of the expression.
27.
Verify the identity.
28.
Find all solutions in the interval
29.
30. Find the exact value of cos 75176.
Use the fundamental identities to write the
expression in terms of a single trigonometric
function.
21.
Triangle ABC has the given area, angle, and side.
Find the length of the requested side. Round to the
nearest integer.
31.
Triangle ABC has the given measures. If the
triangle has exactly one solution, give the area of
the triangle to two decimal places. If the triangle
does not have exactly one solution, determine how
many solutions there are.
Verify the identity.
22.
Find all solutions of the equation.
32.
33. An airplane left an airport and flew east for 120
miles. Then it turned northward to
When it
was 211 miles from the airport, there was an engine
problem and it turned to take the shortest route back
to the airport. Find
the angle through which the
airplane turned.
34. Use the Law of Sines to solve for
tenth.
to the nearest
35. Given a triangle with
and
what is the length of c? Round your
answer to two decimal places.
How many solutions exist for the triangle?
36.
and
Use Heron's Area Formula to find the area of the triangle. Round the result to the nearest tenth.
37.
38. A ship travels due west for 80 miles. It then travels in a northern direction for 61 miles and ends up 129 miles from
its original position. How many degrees did it turn when it changed direction? Round your answer to the nearest
tenth.
Use the Law of Cosines to find the length of the diagonal of the parallelogram.
39.
Use the Law of Cosines to find angle in the
parallelogram. Round to the nearest tenth of a
degree.
Classify the graph of the equation as a circle, a
parabola, an ellipse, or a hyperbola.
46.
40.
41. Draw a plane on the following diagram so that the
intersection of the plane with the double-napped
cone is a parabola.
47.
Find the equations of the asymptotes of the
hyperbola.
48.
Find the standard form of the equation of the
specified hyperbola.
49.
50. Vertices58
42. A parabolic television dish antenna is 16 feet across
at its opening and 11 feet deep. If the receiver is
placed at the focus, how far is it from the vertex?
43. Find the standard form of the equation of the
parabola. ____________________
Vertex: (0, 0); Focus: at (0, 6)
44. A skating park has a track shaped like an ellipse. If
the length of the track is 86 m and the width of the
track is 40 m, find the equation of the ellipse.
Find the standard form of the equation of the
specified ellipse.
45. Center58
length 6
Vertex58
Minor axis of
Asymptotes58
Analysis Final Exam Review B
Answer Section
1.
2. ANS:
150176
3. ANS:
3.351
4. ANS:
Positive coterminal angle58
Negative coterminal angle58 –
5. ANS:
6. ANS:
7. ANS:
5.5030
8. ANS:
Answers may vary. Sample answer58 1
9. ANS:
50.36 m
10. ANS:
11. ANS:
12. ANS:
13. ANS:
14. ANS:
,
15. ANS:
16. ANS:
,
,
17. ANS:
Answers may vary. Sample answer58
18. ANS:
Answers may vary. Sample answer58
,
19. ANS:
Answers may vary. Sample answer58
,
.
20. ANS:
21. ANS:
22. ANS:
Answers will vary.
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25. ANS:
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27. ANS:
28. ANS:
Answers will vary.
29. ANS:
p, p
p
30.
31. ANS:
32. ANS:
There are no solutions.
33. ANS:
147.9176
34. ANS:
27.3
35. ANS:
3.57
36. ANS:
There is exactly 1 solution.
37. ANS:
??
38. ANS:
39. ANS:
14.5
40. ANS:
62.4176
41. ANS:
Answers may vary. Sample answer58
42. ANS:
1.45 ft
43. ANS:
44. ANS:
45. ANS:
46. ANS:
Ellipse
47. ANS:
Parabola
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50. ANS: