How do you find an equation of the tangent line to the curve at the given point $f (x) = sin (cos x)$ $f(x) = sin(cosx)$ and $x = \frac{π}{2}$ $x=pi/2$ ?

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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.

$f (\frac{π}{2}) = sin (cos (\frac{π}{2})) = sin (0) = 0$ $f(pi/2)=sin(cos(pi/2))=sin(0) = 0$

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

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

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

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

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

$y=-x+pi/2$

How do you find an equation of the tangent line to the curve at the given point f(x) = sin(cosx) f(x)=sin(cosx)f(x) = sin(cosx) and x=pi/2x=π2x=pi/2?