Analysis Final Exam Review B
1.Sketch a positive angle with its terminal side in Quadrant IV.
Express the angle in degree measure.
2.
Convert the measure from degrees to radians. Round to three decimal places.
3.192176
Find one positive angle and one negative angle that arecoterminal with the given angle.
4.–
Find the exact value of the six trigonometric functions of thegiven in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.)
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
6.Iffind
Use a calculator to evaluate the function. Round your answer to four decimal places. (Be sure the calculator is in the correct angle mode.)
7.
Use the fundamental trigonometric identities to determine a simplified form of the expression.
8.
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 andFind
Rewrite the indicated trigonometric function in terms of the angle's reference angle. Use the same function.
13.
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.
16., on the interval
Sketch a graph of the function that has the given amplitude and period.
17.Cosine function, ,
Sketch the graph of the function and write equations for 2 consecutive asymptotes.
18.
Sketch the graph of the function and write equations for 2 consecutive asymptotes.
19.
Sketch the graph of the function. Include any asymptotes.
20.
Use the fundamental identities to write the expression in terms of a single trigonometric function.
21.
Verify the identity.
22.
Find all solutions of the equation.
23.
Find all solutions of the equation in the interval
24.
Find all solutions of the equation in the interval
25.
Solve the equation.
26.
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.
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.
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. Findthe angle through which the airplane turned.
34.Use the Law of Sines to solve for to the nearest tenth.
35.Given a triangle withandwhat 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 anglein the parallelogram. Round to the nearest tenth of a degree.
40.
41.Draw a plane on the following diagram so that the intersection of the plane with the double-napped cone is a parabola.
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 Vertex58 Minor axis of length 6
Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.
46.
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
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.
23.ANS:
24.ANS:
25.ANS:
26.ANS:
27.ANS:
28.ANS:
Answers will vary.
29.ANS:
p, pp
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
48.ANS:
49.ANS:
50.ANS: