Find an equation of the tangent line to the curve at the given point. Y=sin(sinx) , (2pi,0)

Question

Find an equation of the tangent line to the curve at the given point.

y = sin(sin x),  (2π, 0)

 

Answer 1

The derivative y'=cosxcos(sinx) by the product rule. At x=2(pi), y'=cos(0)*cos(0)=1, because sin(2(pi))=0. Therefore 1 is the slope of the tangent and the slope of the tangent line y=x+b, where b is the y intercept. Putting in the point (2(pi),0): 0=2(pi)+b, so b=-2(pi) and y=x-2(pi).