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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Number 27

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Step 1

Consider the given diagram for 27.

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.

Step 3

Now, calculate the arc length.

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