What is the equation of the line that is normal to #f(x)=sin^2x+e^xcotx # at # x=pi/3#?
It helps to know some trig derivatives:
First, take the derivative of
That's the slope of the tangent line but we need the slope perpendicular to that which is simply the negative reciprocal.
We also need the point at
Now we can use point-slope form to find the equation of the normal line: