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Chapter 9: Q. 24 (page 775)

The arc length of polar functions: Find the arc lengths of the following polar functions.r=acos胃

, where is a positive constant, for

Short Answer

Expert verified

The arc length is2a蟺units

Step by step solution

01

Given information.

r=acos胃and胃鈭�0,2蟺

02

Arc length.

The length of an arc is given by,

L=鈭�伪尾r2+drd胃2d胃

So,

role="math" localid="1662989532460" L=鈭�02蟺a2cos2胃+-asin胃2d胃鈭�drd胃=-asin胃=鈭�02蟺a2cos2胃+a2sin2胃d胃=鈭�02蟺ad胃鈭�cos2胃+sin2胃=1=2a蟺-0=2a蟺units

Thus, the arc length is2a蟺units

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Most popular questions from this chapter

In Exercises 48鈥�55 convert the equations given in rectangular coordinates to equations in polar coordinates.

y=x+1

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.

r=31+cos胃

In Exercises 48鈥�55 convert the equations given in rectangular coordinates to equations in polar coordinates.

y=x

Use Cartesian coordinates to express the equations for the hyperbolas determined by the conditions specified in Exercises 38鈥�43.

foci(卤6,0), directricesx=卤1

In exercises 31-36 find a definite integral that represents the length of the specified polar curve, and then use a graphing calculator or computer algebra system to approximate the value of integral

Onepetalofthepolarroser=cos2胃
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