# 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?

Nov 22, 2016

Take the derivative.
Use the solution to write a new equation.

#### Explanation:

$f \left(\frac{\pi}{2}\right) = \sin \left(\cos \left(\frac{\pi}{2}\right)\right) = \sin \left(0\right) = 0$

$f ' \left(x\right) = - \sin x \left(\cos \left(\cos x\right)\right)$

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

$= - \left(1\right) \left(\cos \left(0\right)\right) = - 1 = m$

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y - 0 = - 1 \left(x - \frac{\pi}{2}\right)$

$y = - x + \frac{\pi}{2}$