12.3.67 Find the length of the cardioid r 5-5 cos 0. The length of the cardioid is (Simplify your answer.) ro5-5cose 2=7 *=rcose -5cరత)(e 5రి-5 e 5n€ - 5 (66ది swr® du. ఉ",&8 3) " . ఊ కర త) de) (-5sm© - 6@dc©$n€) (5cebb- (5(+Ine)sn© + $uD3 © ర ఒ 5n© 4 1DC0ి Sind 4 (5tఆలి + కn8 - 56©€) 5n6+ 5 S26+ (5ccరి - 5ఆరజయ 2. (256n>© - 50sine sin2+25 Sin2@¥{ 25c© - 5ాతాల ని 25cos2 20)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 43E
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Hello, 

I am trying to find the arc length of r=5-5cos(theta). I am getting stuck on trigonometry identities to simplify the square root and I don't know how to continue the integral. Is there some other way to approach this?

I have attached the problem and my work. 

Thank you.

12.3.67
Find the length of the cardioid r 5-5 cos 0.
The length of the cardioid is
(Simplify your answer.)
Transcribed Image Text:12.3.67 Find the length of the cardioid r 5-5 cos 0. The length of the cardioid is (Simplify your answer.)
ro5-5cose 2=7
*=rcose
-5cరత)(e
5రి-5 e
5n€ - 5 (66ది swr®
du.
ఉ",&8
3) " . ఊ కర
త)
de)
(-5sm© - 6@dc©$n€) (5cebb- (5(+Ine)sn© + $uD3 © ర
ఒ
5n© 4 1DC0ి Sind
4 (5tఆలి + కn8 - 56©€)
5n6+ 5 S26+ (5ccరి - 5ఆరజయ
2.
(256n>© - 50sine sin2+25 Sin2@¥{ 25c© - 5ాతాల
ని
25cos2 20)
Transcribed Image Text:ro5-5cose 2=7 *=rcose -5cరత)(e 5రి-5 e 5n€ - 5 (66ది swr® du. ఉ",&8 3) " . ఊ కర త) de) (-5sm© - 6@dc©$n€) (5cebb- (5(+Ine)sn© + $uD3 © ర ఒ 5n© 4 1DC0ి Sind 4 (5tఆలి + కn8 - 56©€) 5n6+ 5 S26+ (5ccరి - 5ఆరజయ 2. (256n>© - 50sine sin2+25 Sin2@¥{ 25c© - 5ాతాల ని 25cos2 20)
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