478CHAPTER 7 The Trigonometric Functions25. In a circle of radius 1 cm, the area of a certain sector isTT/5 cm². Find the radian measure of the central angle.Express the answer in terms of 7 rather than as a decimalapproximation.26. In a circle of radius 3 m, the area of a certain sector is20 m². Find the degree measure of the central angle. Roundthe answer to two decimal places.In Exercises 27 and 28, find (a) the perimeter of the sector; andHing(b) the area of the sector. In each case, use a calculator to eval-uate the answer and round to two decimal places.27.28.3 m135°Fi30°385 in.0039In Exercises 29–34, you are given the rate of rotation of awheel as well as its radius. In each case, determine the follow-40ing: (a) the angular speed, in units of radians/sec; (b) the linearspeed, in units of cm/sec, of a point on the circumference of thewheel; and (c) the linear speed, in cm/sec, of a point halfwaybetween the center of the wheel and the circumference.Inro29. 6 revolutions/sec; r = 12 cm30. 15 revolutions/sec; r = 20 cm10909lene

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Asked Feb 22, 2020
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Number 27

478
CHAPTER 7 The Trigonometric Functions
25. In a circle of radius 1 cm, the area of a certain sector is
TT/5 cm². Find the radian measure of the central angle.
Express the answer in terms of 7 rather than as a decimal
approximation.
26. In a circle of radius 3 m, the area of a certain sector is
20 m². Find the degree measure of the central angle. Round
the answer to two decimal places.
In Exercises 27 and 28, find (a) the perimeter of the sector; and
Hing
(b) the area of the sector. In each case, use a calculator to eval-
uate the answer and round to two decimal places.
27.
28.
3 m
135°
Fi
30°
38
5 in.
00
39
In Exercises 29–34, you are given the rate of rotation of a
wheel as well as its radius. In each case, determine the follow-
40
ing: (a) the angular speed, in units of radians/sec; (b) the linear
speed, in units of cm/sec, of a point on the circumference of the
wheel; and (c) the linear speed, in cm/sec, of a point halfway
between the center of the wheel and the circumference.
In
ro
29. 6 revolutions/sec; r = 12 cm
30. 15 revolutions/sec; r = 20 cm
10909lene
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478 CHAPTER 7 The Trigonometric Functions 25. In a circle of radius 1 cm, the area of a certain sector is TT/5 cm². Find the radian measure of the central angle. Express the answer in terms of 7 rather than as a decimal approximation. 26. In a circle of radius 3 m, the area of a certain sector is 20 m². Find the degree measure of the central angle. Round the answer to two decimal places. In Exercises 27 and 28, find (a) the perimeter of the sector; and Hing (b) the area of the sector. In each case, use a calculator to eval- uate the answer and round to two decimal places. 27. 28. 3 m 135° Fi 30° 38 5 in. 00 39 In Exercises 29–34, you are given the rate of rotation of a wheel as well as its radius. In each case, determine the follow- 40 ing: (a) the angular speed, in units of radians/sec; (b) the linear speed, in units of cm/sec, of a point on the circumference of the wheel; and (c) the linear speed, in cm/sec, of a point halfway between the center of the wheel and the circumference. In ro 29. 6 revolutions/sec; r = 12 cm 30. 15 revolutions/sec; r = 20 cm 10909lene

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Expert Answer

Step 1

Consider the given diagram for 27.

Trigonometry homework question answer, step 1, image 1

Step 2

Consider the formula to calculate the perimeter, area for the sector of a circle and the length for the length of the arc.

Trigonometry homework question answer, step 2, image 1

Step 3

Now, calculate the arc length.

Trigonometry homework question answer, step 3, image 1

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