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Find the length of the arc if f(x) = In(cos x) and 0 s x %3D 2. Find the length of the arc formed by x (y-1) in the interval 2 sys 9. %3D

Find the length of the arc if f(x) = In(cos x) and 0 s x %3D 2. Find the length of the arc formed by x (y-1) in the interval 2 sys 9. %3D

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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1. Find the length of the arc if f(x) = In(cos x) and 0 s x %3D 2. Find the length of the arc formed by x (y-1) in the interval 2 Sys9.
Transcribed Image Text:1. Find the length of the arc if f(x) = In(cos x) and 0 s x %3D 2. Find the length of the arc formed by x (y-1) in the interval 2 Sys9.
Expert Solution
Part(1) Step 1

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.

y=\ln \left(\cos \left(x\right)\right)

take derivative

y'=\frac{d}{dx}\left(\ln \left(\cos \left(x\right)\right)\right)

y'= \frac{1}{\cos \left(x\right)}\frac{d}{dx}\left(\cos \left(x\right)\right)

y'= \frac{1}{\cos \left(x\right)}\left(-\sin \left(x\right)\right)

y'= -\frac{\sin \left(x\right)}{\cos \left(x\right)}

y'= -\tan \left(x\right)

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