`y = sin(sin(x)), (pi, 0)` Find an equation of the tangent line to the curve at the given point.

Textbook Question

Chapter 3, 3.4 - Problem 53 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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growley52 | College Teacher | (Level 1) Adjunct Educator

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`y = pi - x` is the exact answer.

At `x = pi` ``

`y = sin(sin(pi)) = sin(0) = 0`

`y' = 1/2 (cos(x - sin(x)) + cos(x + sin(x))) = 1/2(cos(pi) + cos (pi))`

=-1.  So y = -x + pi, using the slope intercept form.

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