Name: ________________________ Class: ___________________ Date: __________ ID: A

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PreCalculus: Semester 2 Final Exam Study Guide

Short Answer

1. Draw the angle.

-

2. Convert the angle to a decimal in degrees.

Round the answer to two decimal places.

22°54'35''

3. Convert the angle to D° M' S'' form. Round the

answer to the nearest second.

183.82°

4. If s denotes the length of the arc of a circle of

radius r subtended by a central angle θ, find the

missing quantity. Round to one decimal place, if

necessary.

r = 14.8 inches, θ = 315°, s = ?

5. Convert the angle in degrees to radians. Express

the answer as multiple of ππππ.

54°

6. Convert the angle in radians to degrees.

7. If A denotes the area of the sector of a circle of

radius r formed by the central angle θ, find the

missing quantity. If necessary, round the answer

to two decimal places.

r = 7 feet, A = 56 square feet, θ = ?

8. In the problem, t is a real number and P = (x, y)

is the point on the unit circle that corresponds to

t. Find the exact value of the indicated

trigonometric function of t.

( , ) Find sec t.

9. Find the exact value. Do not use a calculator.

sin 2π

10. Find the exact value. Do not use a calculator.

csc (- )

11. Find the exact value of the expression. Do not

use a calculator.

tan - cos

12. A point on the terminal side of an angle θ is

given. Find the exact value of the indicated

trigonometric function of θ.

(3, -2) Find tan θ.

13. Use the fact that the trigonometric functions are

periodic to find the exact value of the

expression. Do not use a calculator.

csc 540°

14. Name the quadrant in which the angle θ lies.

csc θ > 0, sec θ > 0

Name: ________________________ ID: A

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15. In the problem, sin θ and cos θ are given. Find

the exact value of the indicated trigonometric

function.

sin θ = , cos θ = Find sec θ.

16. Find the exact value of the indicated

trigonometric function of θ.

tan θ = , 180°< θ < 270° Find cos θ.

17. Use the even-odd properties to find the exact

value of the expression. Do not use a calculator.

csc (-60°)

18. Use transformations to graph the function.

y = 5 sin x

19. Graph the function.

y = cot x + 1

20. Find the exact value of the expression.

sin-1

21. Find the exact value of the expression. Do not

use a calculator.

sin-1

22. Find the exact value of the expression.

sin

23. Find the exact value of the expression.

tan

24. Find the exact value of the expression.

sin 265° cos 25° - cos 265° sin 25°

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25. Find the exact value under the given conditions.

26. Find the value of the indicated trigonometric

function of the angle θ in the figure. Give an

exact answer with a rational denominator.

Find sec θ.

27. Solve the right triangle using the information

given. Round answers to two decimal places, if

necessary.

a = 8, B = 30°; Find b, c, and A.

28. Solve the problem.

A radio transmission tower is 150 feet tall. How

long should a guy wire be if it is to be attached 5

feet from the top and is to make an angle of 20°

with the ground? Give your answer to the nearest

tenth of a foot.

29. Solve the triangle.

B = 20°, C = 30°, a = 2

30. Two sides and an angle are given. Determine

whether the given information results in one

triangle, two triangles, or no triangle at all.

Solve any triangle(s) that results.

a = 26, b = 20, B = 15°

31. Find the area of the triangle. If necessary, round

the answer to two decimal places.

A = 23°, b = 9,

32. Plot the point given in polar coordinates.

33. The polar coordinates of a point are given. Find

the rectangular coordinates of the point.

(4, 70°) Round the rectangular coordinates to two

decimal places.

34. The letters x and y represent rectangular

coordinates. Write the equation using polar

coordinates (r, θ).

5x + 7y = 9

Name: ________________________ ID: A

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35. Transform the polar equation to an equation in

rectangular coordinates. Then identify and

graph the equation.

r = 2 sin θ

36. Plot the complex number in the complex plane.

-8 + i

37. Find zw or as specified. Leave your answer

in polar form.

z = 10(cos 45° + i sin 45°)

w = 5(cos 15° + i sin 15°)

Find .

38. Write the expression in the standard form a +

bi.

3

39. Find all the complex roots. Leave your answers

in polar form with the argument in degrees.

The complex fifth roots of -2i

40. Use the vectors in the figure below to graph the

following vector.

2u - z - w

41. Find the indicated quantity.

Find u + v given u = -9i - 4j and v = -7i + 9j.

42. Find the quantity if v = 5i - 7j and w = 3i + 2j.

+

43. Use the TABLE feature of a graphing utility to

find the limit.

Name: ________________________ ID: A

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44. Use the graph shown to determine if the limit

exists. If it does, find its value.

f(x)

45. Use the grid to graph the function. Find the

limit, if it exists

f(x), f(x) =

46. Find the limit algebraically.

lim (x - )(x + )

47. Find the one-sided limit.

(x2 - 3x - 5)

48. Determine whether f is continuous at c.

f(x) = ; c = 7

49. Determine whether f is continuous at c.

f(x) = ; c = 1

50. Find the numbers at which f is continuous. At

which numbers is f discontinuous?

f(x) =

51. Find the slope of the tangent line to the graph at

the given point.

f(x) = x2 + 5x at (4, 20)

52. Find the derivative of the function at the given

value of x.

f(x) = x3 + 4x; x = -2

Essay

53. Prove:

ID: A

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PreCalculus: Semester 2 Final Exam Study Guide

Answer Section

SHORT ANSWER

1. ANS:

PTS: 1

2. ANS:

22.91°

PTS: 1

3. ANS:

183°49'12''

PTS: 1

4. ANS:

81.4 in.

PTS: 1

5. ANS:

PTS: 1

6. ANS:

36°

PTS: 1

7. ANS:

2.29 radians

PTS: 1

8. ANS:

PTS: 1

ID: A

2

9. ANS:

0

PTS: 1

10. ANS:

0

PTS: 1

11. ANS:

-

PTS: 1

12. ANS:

-

PTS: 1

13. ANS:

undefined

PTS: 1

14. ANS:

I

PTS: 1

15. ANS:

PTS: 1

16. ANS:

-

PTS: 1

17. ANS:

2

PTS: 1

ID: A

3

18. ANS:

PTS: 1

19. ANS:

PTS: 1

20. ANS:

PTS: 1

21. ANS:

PTS: 1

ID: A

4

22. ANS:

PTS: 1

23. ANS:

2 -

PTS: 1

24. ANS:

-

PTS: 1

25. ANS:

PTS: 1

26. ANS:

sec θ =

PTS: 1

27. ANS:

b = 4.62

c = 9.24

A = 60°

PTS: 1

28. ANS:

424.0 ft

PTS: 1

29. ANS:

A = 130°, b = 0.89, c = 1.31

PTS: 1

30. ANS:

two triangles

A1 = 19.66°, C1 = 145.34°, c1 = 43.95 or

A2 = 160.34°, C2 = 4.66°, c2 = 6.28

PTS: 1

ID: A

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31. ANS:

3.52

PTS: 1

32. ANS:

PTS: 1

33. ANS:

(1.37, 3.76)

PTS: 1

34. ANS:

r(5 cos θ + 7 sin θ) = 9

PTS: 1

35. ANS:

x2 + (y - 1)2 = 1; circle, radius 1, center at (0, 1) in rectangular coordinates

PTS: 1

ID: A

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36. ANS:

PTS: 1

37. ANS:

2(cos 30° + i sin 30°)

PTS: 1

38. ANS:

-4 - 4 i

PTS: 1

39. ANS:

(cos 54° + i sin 54°), (cos 126° + i sin 126°), (cos 198° + i sin 198°), (cos 270° + i sin 270°),

PTS: 1

40. ANS:

PTS: 1

41. ANS:

-16i + 5j

PTS: 1

ID: A

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42. ANS:

+

PTS: 1

43. ANS:

2

PTS: 1

44. ANS:

2

PTS: 1

45. ANS:

-1

PTS: 1

46. ANS:

-5

PTS: 1

47. ANS:

-1

PTS: 1

48. ANS:

not continuous

PTS: 1

49. ANS:

not continuous

PTS: 1

50. ANS:

continuous for all real numbers except x = -2 and x = 2

PTS: 1

51. ANS:

13

PTS: 1

52. ANS:

16

PTS: 1

ID: A

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ESSAY

53. ANS:

PTS: 1