What is the equation of the tangent line of #r=cos(theta+pi/2)*cos(theta-pi) # at #theta=(-pi)/8#?
Simplify before you differentiate.
By the Cosine Sum Formula
By the Cosine Difference Formula
Their product is
By the Sine Double angle formula, we have
To find the slope of the tangent line, use the fact that
Finally, determine the point (x, y) corresponding to the point that you are interested in, where