Question

Find an equation of the tangent line to the curve at the given point. y = sin(sin(x)), (3π, 0)

Answer 1

Use the chain rule to get the derivative (the slope), then use the given point to write the equation.

y = sin(sinx)

dy/dx = cos(sinx) cos(x)

x = 3π

sin(3π) = 0

cos(sin(3π)) = cos(0) = 1

cos(3π) = -1

m = dy/dx|x=3π = -1

y = -x + b

0 = -3π + b

b = 3π

y = -x + 3π