How do you find an equation of the tangent line to the curve at the given point #f(x) = sin(cosx) # and #x=pi/2#?

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Answer 1 · 2016-11-22T03:57:27

Take the derivative.
Plug in your x-value.
Use the solution to write a new equation.

#f(pi/2)=sin(cos(pi/2))=sin(0) = 0#

#f'(x) = -sinx(cos(cosx))#

#f'(pi/2) = -sin(pi/2)(cos(cos(pi/2))#

#=-(1)(cos(0))=-1=m#

#y-y_1 = m(x-x_1)#

#y-0=-1(x-pi/2)#

#y=-x+pi/2#