Find the equation of the tanget line

Question

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