Brix S.

asked • 04/29/21

Finding The Arc Length

Find the length of arc of r= asin θ +b cos θ

1 Expert Answer

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Rachel A. answered • 04/30/21

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arc length =∫√(r2+(dr/dθ)2)dθ

 r= asin θ +b cos θ

dr/dθ=acosθ-bsinθ

∫√((asinθ+bcosθ)2+(acosθ-bsinθ)2)dθ

(asinθ+bcosθ)2+(acosθ-bsinθ)2=a2sinθ2+2abcosθsinθ+b2cosθ2+a2cosθ2-2abcosθsinθ+b2sinθ2=a2+b2

∫√(a2+b2)dθ=θ√(a2+b2)+Constant

θ√(a2+b2)+Constant is your answer

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