Trigonometry Final #1 - Sandy Bele · Use algebra and the fundamental trigonometric identities. Your answer should be a number or use a single trigonometric function. 25.Complete

ALEKS Trigonometry Final #1 - 11/19/2014 12:45:44 PM PST - Copyright © 2014 UC Regents and ALEKS Corporation. P. 1/25

Trigonometry Final #1

Trigonometry / Trigonometry (Prof. Belew)

Student Name/ID:

1.

Sketch in standard position.

2. Answer the following.

(a) Find an angle between and that is coterminal with

(b) Find an angle between and that is coterminal with

Give exact values for your answers.


3. A circle has a radius of Find the radian measure of the central angle that intercepts an arc of

length

Do not round any intermediate computations, and round your answer to the nearest tenth.

4. A right triangle has side lengths and as shown below.

Use these lengths to find and

5.

Find the exact value of

6. Suppose that is an angle in standard position whose terminal side intersects the unit circle at

Find the exact values of and


7. Find the exact values below.

8. For the right triangles below, find the exact values of the side lengths and

If necessary, write your responses in simplified radical form.


9. Find where is the angle shown.

Give an exact value, not a decimal approximation.

10. Find and where is the angle shown in the figure.

Give exact values, not decimal approximations.

11. Solve for in the triangle. Round your answer to the nearest tenth.


12. A kite is flying off the ground, and its line is pulled taut. The angle of elevation of the kite is

Find the length of the line. Round your answer to the nearest tenth.

13. Find the angle of depression from the top of a lighthouse that is above water level to the

waterline of a ship off shore. Round your answer to the nearest tenth of a degree.

14.

Find the reference angle for

15.

Let be an angle in quadrant such that



16.

Let be an angle in quadrant such that


17.

Graph the function

18.

Graph the function


19.

Graph the function


20. Three graphs are given below.For each, choose its equation from the following.



21.

Graph the function

22. Graph the function

23.

Find the exact value of

Write your answer in radians in terms of


24. Simplify.

Use algebra and the fundamental trigonometric identities.Your answer should be a number or use a single trigonometric function.

25. Complete the proof of the identity by choosing the Rule that justifies each step.

26. Prove the identity.

27. Prove the identity.

28. Find the exact value of by using a sum or difference formula.


29. Use a sum or difference formula to find the exact value of the following.

30.

Find and if and terminates in quadrant

31. Simplify the expression by using a double-angle formula.

32. Find all solutions of the equation in the interval


If there is more than one solution, separate them with commas.

33. Find all solutions to the equation.


Example: , or ,














38. Consider a triangle like the one below. Suppose that and (The figure

is not drawn to scale.) Solve the triangle.

Round your answers to the nearest tenth.

39. Consider a triangle like the one below. Suppose that and (The figure is

not drawn to scale.) Solve the triangle.

Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.


40. Consider a triangle like the one below. Suppose that and (The figure is

not drawn to scale.) Solve the triangle.

Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.

41. Find the magnitude of the vector

Write your answer in simplified radical form.

42. Given the vector shown below, construct the vector having initial point


43. Given the vectors and find and

44. Given vectors and find

45. Construct the vector having initial point


46. Find the magnitude of the vector given below. Also find the measure (in degrees) of the acute angle

formed by the vector and the -axis. Do not round any intermediate computations, and round your

responses to decimal places.

47. Calculate the and components of the vector given below. Do not round any intermediate

computations, and round your responses to decimal places.


48. Write the complex number in trigonometric form (sometimes called polar form), with the

angle expressed in radians from to Do not round any intermediate computations, and round the

values in your answer to decimal places.

49.Use De Moivre's theorem to find Put your answer in standard form.

50. Write the complex number in trigonometric form (sometimes called polar form), with the

angle expressed in radians from to Do not round any intermediate computations, and round the

values in your answer to decimal places.


Trigonometry Final #1 Answers for class Trigonometry / Trigonometry

1.

2.

(a)

radians

(b)

3. radians

4.

5.

6.


7.

8.

9.

10.

11.

12.

13.

14.

15.

16.


17.

18.

19.

20.


21.

22.

23.

24.

25. Statement Rule

Pythagorean

Reciprocal

Algebra

Quotient


26. Statement Rule

Pythagorean

Quotient

Algebra

27. Statement Rule

Reciprocal

Algebra

Pythagorean

Algebra

Quotient

28.

29.

30.

and

31.

32.

33.


34.

, , ,

35.

36.

, , ,

37. ,

38.

39. , , ,

or , ,

40. , ,

41.

42.

43.

44.

45.


46. magnitude of the vector:

47.

48.

49.

50.

Trigonometry Final #1 - Sandy Bele · Use algebra and the fundamental trigonometric identities. Your answer should be a number or use a single trigonometric function. 25.Complete

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