PrecalculusChapter 5 Review

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Convert the angle to a decimal in degrees. Round the answer to two decimal places.

1) 65°44'30" 1)

Convert the angle to D° M' S" form. Round the answer to the nearest second.

2) 258.81° 2)

If s denotes the length of the arc of a circle of radius r subtended by a central angle 6, find the missing quantity.

3) r = 12.05 centimeters, 9 = 4 radians, s = ? 3)

4) r = -| feet, s = 10 feet, 9 = ? 4)O

Solve the problem.

5) The minute hand of a clock is 4 inches long. How far does the tip of the minute hand move 5)in 45 minutes? If necessary, round the answer to two decimal places.

Convert the angle in degrees to radians. Express the answer as multiple of it.

6) -105° 6)

7) 6° 7)

Convert the angle in radians to degrees.

8) - 8)

Solve the problem.

10) A circle has a radius of 4 centimeters. Find the area of the sector of the circle formed by an 10)angle of 25°. If necessary, round the answer to two decimal places.

Draw the angle.

11) -- 11)

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 ofthe indicated trigonometric function of t.

12) ( , - - ) Find sin t. 12)

13) (f' 9 > Find tan t. 13)

1 4 ) ( , ) Find sect. 1 4 )

15) ( - , ) Find cost. 15)

16) ( - , ) Find cot t . 16)o o

17)(f'- 9 ) Find csc t. 17)

Find the exact value. Do not use a calculator.18) sec(-jt) 18)

19) cot2ir 19)

20) sinO 20)

21) tan(39it) 21)

Find the exact value of the expression. Do not use a calculator.

22) sec 60° - cos 30° 22)

23) cot -J- sin -J 23)O J

24) cos 120° tan 60° 24)

A point on the terminal side of an angle 0 is given. Find the exact value of the indicated trigonometric function of 6.25) (-5,-12) Find sine. 25)

Solve the problem.26) If cos 9 = -0.9, find the value of cos 6 + cos (9 + 2n) + cos (9 + 4;t). 26)

27) If tan Q = 0.6, find the value of tan 9 + tan (9 + n) + tan (9 + 2it). 27)

Name the quadrant in which the angle 0 lies.28) sec 9 < 0, tan 9 < 0 28)

Find the exact value of the indicated trigonometric function of 0.

29) esc 9 = -—, 9 in quadrant III Find cot 9. 29)

Use the even-odd properties to find the exact value of the expression. Do not use a calculator.30) sec(-jt) 30)

3D tanf-^1 31)I J

32) sin[--|] 32)

33) cos (-30°) 33)

Find the exact value of the indicated trigonometric function of 6.

34) sin 8=—, sec9<0 Find cos 9 and tan 6. 34)

35) cos9=|i -y<9<2jt Find cot 9. 35)

36) tan9 = - - , 9 in quadrant II Find cos 9. 36)

Use the properties of the trigonometric functions to find the exact value of the expression. Do not use a calculator.37) sec2 89° - tan2 80° 37)

38) sin2 89° + cos2 89° 38)

In the problem, sin 0 and cos 0 are given. Find the exact value of the indicated trigonometric function./7 1

39) sin 0 = ̂ -, cos 9 = 4 Find esc 0. 39)4 4

49) sin 9 =\, cos 8=-^- Find tan 0. 49)4 4

Solve the problem.41) Determine the sign of the trigonometric values listed below. 41)

(i) sin 259°(ii) tan 330°(iii) cos(-49°)

Name the quadrant in which the angle 0 lies.42) tan0>0, s in0<0 42)

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator.43) esc 699° 43)

44) sec—— 44)

45) cos^ 45)J

46) sin 495° 46)

Solve the problem.

47) What is the range of the cotangent function? 47)

48) What is the range of the sine function? 48)

49) For what numbers 9 is f(0) = cot 9 not defined? 49)

3

50) For what numbers 0 is f(0) = tan 0 not defined?

51) What is the domain of the cosine function?

52) If sin 0 = 0.6, find sin (0 + n).

50)

51)

52)

A point on the terminal side of an angle 6 is given. Find the exact value of the indicated trigonometric function of 0.

53) (-4,-!) Find sec 0. 53)

54) (3,2) Find tan 0.

Use a calculator to find the approximate value of the expression rounded to two decimal places.

55) cot

54)

55)

r:r\) sec — 56)

57) tan 78°

58) cos 52°

59) sin 40°

Find the exact value of the expression. Do not use a calculator.60) sin 330° sin 270°

Use transformations to graph the function.61) y = 5 sin x + 1

10--y

H H H 1 1 1 1—

Ji 2ji 3jt-2'

-4

-6

-8'

-10--

Write the equation of a sine function that has the given characteristics.62) Amplitude: 3

Period: 6it

Find the phase shift of the function.

63) y = 5 cos (6x + it)

57)

58)

59)

60)

61)

62)

63)

Use transformations to graph the function.

64) y = -3 sin (x + —)

J.y

H H

-2--

-6--

65) y = 4 cos x - 5

(,-•

4--

2 - -

h

-2--

-4--

-6--

-8--

-10--

H h

Solve the problem.

64)

H 1 1 1 1 h

65)

1 .66) For the equation y = - — sin(4x + Sit), identify (i) the amplitude, (ii) the phase shift, and (iii) 66)

the period.

Write the equation of a sine function that has the given characteristics.67) Amplitude: 3 67)

Period: 4jt

Phase Shift: -^4

Solve the problem.

68) For the equation y = ~j cos(2x - 2it), identify (i) the amplitude, (ii) the phase shift, and (iii) 68)

the period.

Use transformations to graph the function.

69) y = -5 cos (x - —)

Jy

4- •

2 - -

-2- •

.4. .

-6- •

H h

;i 2n

Write the equation of a sine function that has the given characteristics.

70) Amplitude: 4Period: 5

69)

70)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Without graphing the function, determine its amplitude or period as requested.

71) y = -5 cos —x Find the period.J

A)-5 B)6ir O-

71)

72) y = sin 3x

A) 2n

Find the period.

B) - C)3

72)

Find an equation for the graph.73)

A) y = 5 sin (3x) C) y = 3 sin (5x) D) y = 5 sin —x

73)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Match the given function to its graph.

74) 1) y = sin (x --j) 2) y = cos (x +-|) 74)

3) y = sin (x + —) 4) y = cos (x - —)

A

Find the phase shift of the function.

75) y = -4sinUx--j

76) y = -2cos x + 44

77) y = 3sin x-

D

75)

76)

77)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Without graphing the function, determine its amplitude or period as requested.78) y = -4 sin x Find the amplitude.

A) 4 B)-4jr C)2:t D)-4

78)

Find an equation for the graph.79)

A) y = 2 sin (5x) B) y = 5 sin —x C) y = 5 sin (2x) = 2 s i n x

80)

A) y = 2 cos (4x) 2cos[jx| C) y = 4 cos (2x) D) y = 4 cos —x

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

81)

Graph the function.81) y = 3tan(4x)

6- •

4- •

2- •

-2- •

-4- •

-6--

H 1it 3it _ 57i2 * T 2* T

79)

80)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Match the given function to its graph.

82) l)y = 2 + sinx 2)y = 2 + cosx 82)3) y = -2 + sin x 4) y = -2 + cos xA B

c

I—h

A) 1A, 2C, 3D, 4B B) 1A, 2B, 3C, 4D C) 1A, 2D, 3C, 4B

H 1 h-

n 2it

D) IB, 2D, 3C, 4A

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

83)

Graph the function.

83) y = -cot(nx)

*..y

-" ' -2:-4-

-6-

1 1 1 1 1 1 #

' f * f 2* ^ 3* "

84) y = -2tan

-2+

H 1 h331 „ 531 , Xy 23, y 3lt

84)

= lcotfx-f]

-31 I

1 1

85)

86) y =

10+y

4J2-

t 1 1 F 1

-231 -31 _2_

-4-

-6-

'

-10-^

XJi 2̂ ;

86)

10

87) y = 4sec|yx]

10+y

87)

64^2-

-2-

-4-

-6-

H 1 1 1 1 1 1 1—2n 4jr (m Sit

-10+

Graph the function. Show at least one period.

88) y = 4sin(43tx

-l

89) y = 2cod

88)

89)

-Ti-2-

-4-

-6-

-8-\t 2jt 3it

11

90) y = -5sin

3 - - y

90)

H 1 h

91) y = 5cos -3x+y 91)

H 1 h

Solve the problem.92) A town's average monthly temperature data is represented in the table below: 92)

Month, xJanuary, 1February, 2March, 3April, 4May, 5June, 6July, 7August, 8September, 9October, 10November, 11December, 12

Average MonthlyTemperature, °F

30.635.344.260.071.183.386.081.381.359.344.832.6

Find a sinusoidal function of the form y = A sin (cox -((>) + B that fits the data.

12

93) An experiment in a wind tunnel generates cyclic waves. The following data is collected for56 seconds:

93)

Time(in seconds)

0142842

Wind speed(in feet per second)

17416541

56 17

Let V represent the wind speed (velocity) in feet per second and let t represent the time inseconds. Write a sine equation that describes the wave.

94) The following data represents the normal monthly precipitation for a certain city inCalifornia.

94)

Month, xJanuary, 1February, 2March, 3April, 4May, 5June, 6July, 7August, 8September, 9October, 10November, 11December, 12

Normal MonthlyPrecipitation, inches

6.064.454.382.081.270.560.170.460.912.245.215.51

Draw a scatter diagram of the data for one period. Find a sinusoidal function of the formy = A sin (cox - <t>) + B that fits the data. Draw the sinusoidal function on the scatterdiagram. Use a graphing utility to find the sinusoidal function of best fit. Draw thesinusoidal function of best fit on the scatter diagram.

H 1 1 1 1 h H 1 h

13

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Answer the question.95) Which one of the equations below matches the graph?

2

-2

A) y = 2 sirJ —x

4— TC3

B) y = -2 cos(3x)

96) Which one of the equations below matches the graph?

2

-2

A) y = -2 si•fH

1271

= 2 s i n ( <

r

95)

D) y = -2 sin(3x)

96)

D) y = 2 cos(3x)

14

Answer KeyTestname: PRE CALC CHAPTER 5 REVIEW

1) 65.74°2) 258°48'36"3) 48.2 cm4) 15 radians5) 18.85 in.

8) 288°9) -60°

10) 3.49cm2

11)

13)

14)

15) -

16) -

17) -

-\/772

9^/6565

<\/65

'S/55

65

18) -119) undefined20) 021) 0

4-^/32

22)

23) --

26) -2.727) 1.8

15

Answer KeyTestname: PRE CALC CHAPTER 5 REVIEW

28) II

30) -131) -A/3

32) -f

33)

2135) "20

37) 138) 1

39)

40)15

41) (i) negative(ii) negative(iii) positive

42) III

43, -3

44) -A/2

45) -1

.,, A/246) -y-

47) all real numbers48) all real numbers from -1 to 1, inclusive49) integral multiples of n (180°)

50) odd multiples of -| (90°)

51) all real numbers52) -0.6

55) 3.0856) 1.24

16

Answer KeyTestname: PRE CALC CHAPTER 5 REVIEW

57) 4.7058) 0.6259) 0.64

62) y = 3 sin —xI3 J

63) -£• units to the left6

17

Answer KeyTestname: PRE CALC CHAPTER 5 REVIEW

65)

10- -y

66) (i)

67) y = 3sin — x - — it

70) y = 4sin —;I 5

71) B72) B73) D74) 1C,2A,3B,4D

75) — units to the right

76) — units to the left4

77) — units to the right

78) A

18

Answer KeyTestname: PRE CALC CHAPTER 5 REVIEW

19

Answer KeyTestname: PRE CALC CHAPTER 5 REVIEW

85)

..y

4 - -

2- -

H P

-2--

-4--

-6--

3ii2 f

86)

10--y

«—I 1 1 H

-23i

10-•

87)

H 1 H

31 2jl

0- -y.

H h-2jt -f- 2ji 4n 6re Sit x

-2'

-4-

-6-

-10--

20

Answer KeyTestname: PRE CALC CHAPTER 5 REVIEW

21

Answer KeyTestname: PRE CALC CHAPTER 5 REVIEW

92) y = 27.7 sin f-x - —1 + 58.316 J

93) V = 24 sin -^t-1 +41

94) y = 3.14 sin (0.46x + 1.52) + 3.16

n'«J

95) D96) C

22