accelerated integrated...

Accelerated Integrated Precalculus Name _______________________

4.1a Homework Sheet

Determine the quadrant in which each angle measure lies.

1. 87.9 2. 8.5 3. 282 4. 675

5. 7

4

6.

11

4

7. 3.5 radians 8. 2.25 radians

Sketch the angle in standard position.

9. 780 10. 450 11. 11

6

12.

2

3

Determine two coterminal angles (one positive and one negative) for each angle.

13. 14.

15. 9

4

16.

2

15

17. 36 18. 546

Find (if possible) the complement and supplement of the angle.

19. 24 20. 2

3

21.

3

Rewrite each angle in radian measure as a multiple of .

22. 30 23. 120

24. 83.7 25. 216.35

Rewrite each angle in degree measure.

26. 3

2

27. 4

28. 4.2 29. 2

31 in

12 in60 ft

75 ft


4.1b Homework Sheet p.266-268 #59,61,62-63,65-69 odd,70,72,74,79,82-85,87-88,97,99,102,103

Convert the angle measure to decimal degree form. Round to four decimal places if necessary.

59. 64 45' 61. 85 18'30" 62. 408 16'25" 63. 125 36"

Convert the angle measure to ' "D M S form. (Be sure all measurements are in degree form first.)

65. 280.6 67. 345.12 69. 0.355 70. 0.7865

Find the radian measure of the central angle. (Hint: s r )

72. 74. 79. 14.5 , 35r cm s cm

Find the length of the arc on the circle of radius r intercepted by a central angle .

82. 9 , 60r ft 83.

2

27 ,3

r m radians 84.

3

12 ,4

r cm radians

Find the radius r of a circle with an arc length s and a central angle .

85. s 36ft, radians

2 87. s 82miles, 135 88. s 8in, 330

97. Construction The circular blade on a saw has a diameter of 7.5 inches and rotates at 2400 revolutions

per minute.

A) Find the angular speed in radians per second.

B) Find the linear speed of the saw teeth (in feet per second) as they contact the wood being cut.

99. Angular Speed A computerized spin balance machine rotates a 25-inch diameter tire at 480 revolutions

per minute.

A) Find the road speed (in miles per hour) at which the tire is being balanced.

B) At what rate should the spin balance machine be set so that the tire is being tested for 70 miles per

hour?

True or False? Justify your answer.

102. An angle that measures 1260 lies in Quadrant III.

103. The angles of a triangle can have radian measures 2

, ,3 4 12

.

Accelerated Integrated Precalculus Name _____________________

4.2 Homework Sheet

p. 274-276: 1,3,17-27 odd,31-61 odd,77,78

Determine the exact value of the six trigonometric functions of the angle .

1. 3.

Evaluate (if possible) the sine, cosine, and tangent of the real number.

17. t4

19.

7

6

21.

2t

3

23. 5

t3

25. t

6

27.

7t

4

Evaluate (if possible) the six trigonometric functions of the real number.

31. 3

t4

33. t

2

35.

2t

3

Evaluate the trigonometric function.

37. sin 5 39. 8

cos 3

41. 13

cos 6

43. 9

sin 4

Use the value of the trigonometric function to evaluate the indicated functions.

45. 1

sin t3

47. 1

cos t5

49. 4

sin t5

a) sin t a) cos t a) sin t

b) csc t b) sec t b) sin t

Use a calculator to evaluate the trigonometric expression. Round your answer to four decimal

places.

51. 7

sin 9

53.

11cos

5

55. csc 1.3

57. cos 1.7 59. csc 0.8 61. sec 22.8

True or False? Determine whether the statement is true or false. Justify your answer.

77. Because sin t sint , it can be said that the sine of a negative angle is a negative number.

78. sin a sin a 6


4.3a Homework Sheet

p. 284-286: 1,3,9-15 odd,9-11,13-14, 17-26, 69-75 odd

Find the exact values of the six trigonometric functions of the angle shown in the figure.

1. 3.

Sketch a right triangle corresponding to the trigonometric function of the acute angle . Use the

Pythagorean Theorem to determine the third side of the triangle and then find the other five

trigonometric functions of .

9. 5

sin6

10. cot 5

11. sec 4 13. tan 3

14. 17

csc4

15. 9

cot4

Construct the appropriate triangle (or use the unit circle) to complete the table. 0 90 , 02

.

Function θ (deg) θ (rad) Function Value

17. sin 30

18. cos 45

19. tan

3

20. sec

4

21. cot 3

3

22. csc 2

23. cos

6

24. sin

4

25. cot 1

26. tan 1

3

Find the exact values of the indicated variables (selected from x, y, and r).

69. Find y and r. 71. Find x and y.

73. Find x and r. 75. Find x and r.


4.3b Homework Sheet

p. 285-286: 49-56,77,79,81

Use trigonometric identities to transform one side of the equation into the other.

49. tan cot 1 50. csc tan sec

51. tan cos sin 52. cot sin cos

53. 21 cos 1 cos sin 54. csc cot csc cot 1

55. sin cos

csc sec cos sin

56. 2tan cot

csctan

77. Height A six-foot person walks from the base of a streetlight directly toward the tip of the

shadow cast by the streetlight. When the person is 16 feet from the streetlight and 5 feet

from the tip of the streetlight’s shadow, the person’s shadow starts to appear beyond the

streetlight’s shadow.

a) Draw a right triangle that gives a visual representation of the problem. Show the known

quantities and use a variable to indicate the height of the streetlight.

b) Use a trigonometric function to write an equation involving the unknown quantity.

c) What is the height of the streetlight?

79. Width A biologist wants to know the width w of a river in order to properly set instruments

for studying the pollutants in the water. From point A, the biologist walks downstream 100

feet and sights to point C. From this sighting, it is determined that 58 . How wide is the

river?

81. Angle of Elevation A zip-line steel cable is being constructed for a reality television

competition show. The high end of the zip-line is attached to the top of a 50-foot pole while

the lower end is anchored at ground level to a stake 50 feet from the base of the pole.

a) Find the angle of elevation of the zip-line.

b) Find the number of feet of steel cable needed for the zip-line.

c) A contestant takes 6 seconds to reach the ground from the top of the zip-line. At what

rate is the contestant moving down the line? At what rate is the contestant dropping

vertically?


4.4a Homework Sheet p. 294: 1, 2, 8, 10, 13-16, 19-24

Determine the exact values of the six trigonometric functions of the angle .

1. a) b)

2. a) b)

Each point is on the terminal side of an angle in standard position. Determine the exact value of

the six trigonometric functions of the angle.

8. 24,10 10. 5, 6

State the quadrant in which lies.

13. sin 0 and cos 0 14. sec 0 and cot 0

15. cot 0 and cos 0 16. tan 0 and csc 0

Find the values of the six trigonometric functions of .

Function Value Constraints

19. 15

tan8

sin 0

20. csc 4 cot 0

21. sec 2 0

22. sin 0 3

2 2

23. cot is undefined 3

2 2

24. tan is undefined 2


4.4b Homework Sheet p. 295: 29-44, 55, 56, 61-64, 66-70, 74, 75, 92-94

Evaluate the trigonometric function of each angle.

29. sec 30. tan2

31.

3cot

2

32. csc0 33. sec0 34. 3

csc2

35. cot 36. csc2

Find the reference angle for each angle measure.

37. 120 38. 225 39. 135

40. 330 41. 5

3

42.

3

4

43. 5

6

44.

2

3

Evaluate the sine, cosine, and tangent of the angle without using a calculator.

55. 750 56. 495

61. 11

4

62.

10

3

63. 17

6

64.

20

3

Find the indicated trigonometric value in the specified quadrant.

Function Quadrant Trigonometric Value Function Quadrant Trigonometric Value

66. cot 3 II sin

67. csc 2 IV cot

68. 5

cos8

I sec

69.

9sec

4

III tan

70. 5

tan4

IV csc

Use the given value to find the remaining trigonometric functions of .

74. cot 5 , sin 0 75. 3

csc , tan 02

Find two solutions of the equation. Give your answers in degrees 0 360 and radians

0 2 . Do not use a calculator.

92. a) csc 2 b) csc 2

93. a) 2 3

sec3

b) 1

cos2

94. a) cot 3 b) sec 2


4.5a Homework Sheet

p. 304-305: 27, 28, 30, 47, 48

Sketch the graphs of f and g in the same coordinate plane. Include two full periods.

27. f(x) sinx

g(x) 4sinx

28.

f(x) sinx

xg(x) sin

3

30. f(x) 2cos2x

g(x) cos4x

2

Sketch the graph of each function. Identify the amplitude and period.

47. 2 x

y 2sin3

48. x

y 10cos6


4.5b Homework Sheet

p. 304-305: 15-22, 32, 34, 50, 52, 53, 87, 88

Describe the relationship between the graphs of f and g including amplitudes, periods, and shifts.

15.

f(x) sinx

g(x) sin x

16.

f(x) cosx

g(x) cos x

17. f(x) cos2x

g(x) cos2x

18.

f(x) sin3x

g(x) sin 3x

19. f(x) cosx

g(x) 5cosx

20.

f(x) sinx

1g(x) sinx

2

21. f(x) sin2x

g(x) 5 sin2x

22.

f(x) cos4x

g(x) 6 cos4x

Sketch the graphs of f and g in the same coordinate plane. Include two full periods.

32. f(x) 4sin x

g(x) 4sin x 2

34.

f(x) cosx

g(x) cos x2

Sketch the graph of each function. Identify the amplitude and period.

50. 2 x

y 2 2sin 3

52. y 3cos 6x 53. y 2sin 4x

87. In section 4.2, it was shown that f(x) cosx is an even function and g(x) sinx is an odd

function. Use a graphing utility to graph h and use the graph to determine whether h is even,

odd, or neither.

a) 2h(x) cos x b) 2h(x) sin x c) h(x) sinxcosx

88. If f is an even function and g is an odd function, use the results of Exercise 87 to make a

conjecture about each of the following.

a) 2

h(x) f(x) b) 2

h(x) g(x) c) h(x) f(x) g(x)


4.6a Homework Sheet

p. 316: 5, 7, 15, 17

Graph each function. Include two full periods.

5. 1

y tanx2

7. y 2tan2x

15. 1 x

y cot2 2

17. x

y 2tan4


4.6b Homework Sheet

p. 316-317: 9, 11, 13, 20, 22, 57, 58

Sketch the graph of the function. Be sure to include two full periods.

9. 1sec

2y x 11. sec 3y x

13. 3 csc2

xy

20. secy x 22. csc 2y x

Exploration Use a graphing calculator to graph the function. Use the graph to determine the

behavior of the function as x c .

57. cotf x x

58. cscf x x

(a) As 0x , the value of f x

(b) As 0x , the value of f x

(c) As x , the value of f x

(d) As x , the value of f x

(a) As 0x , the value of f x

(b) As 0x , the value of f x

(c) As x , the value of f x

(d) As x , the value of f x

Accelerated Integrated Precalculus Name___________________

4.7a Homework Sheet

p. 327-328 # 1-9 odd, 35-45 odd

Find the exact value of each expression without using a calculator.

1. a. 1

arcsin2

3. a. arcsin 1

b. arcsin 0 b. arccos 1

5. a. 3

arctan3

7. a. arctan 3

b. arctan 1 b. arctan 3

9. a. 1 3sin

2

b.

1 3tan

3

Use the properties of inverse functions to find the exact value of the expression.

35.

1 11tan tan

6 37.

1 5sin sin

2

39.

1 5sin tan

4 41. tan arcsin 0

43. sin arctan 1 45.

arcsin cos6

Accelerated Integrated Precalculus Name___________________

4.7b Homework Sheet

p. 328-330 # 15-19 odd, 47-53 odd, 55-61 odd, 83, 85

Use a calculator to approximate the value of the expression. Round your answer to the

nearest hundredth.

15. 1cos 0.75 17. arcsin 0.75 19. arctan 6

Find the exact value of the expression. (Hint: Sketch a right triangle.)

47.

4sin arctan

3 49.

24cos arcsin

25

51.

3sec arctan

5 53.

2sin arccos

3

Write an algebraic expression that is equivalent to the given expression. (Hint: Draw a

right triangle or refer to #6 in the notes.)

55. cot arctanx 57. sin arccos x 2

59.

xtan arccos

5 61.

xcsc arctan

7

83. Photography A television camera at ground level is filming the lift-off of a space

shuttle at a point 750 meters from the launch pad. Let be the angle of elevation to the

shuttle and let s be the height of the shuttle.

a) Write as a function of s.

b) Find when s = 400 meters and when s = 1600 meters.

85. Angle of Elevation An airplane flies at an altitude of 6 miles toward a point directly

over an observer. Consider and x as shown in the figure.

a) Write as a function of x.

b) Find when x = 10 miles and x = 3 miles.

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