calculus question help please

Question

Find the exact value of the slope of the line which is tangent to the curve given by the equation

r = 1 - 2cos θ at  . You must show your work.

Answer 1

The slope of a tangent line of a function at a point where the function is continuous is equal to the derivative of the function at that point. So r'= (-2)(-sin θ) =2 sin θ Thus, at π/2 r'=2 sin (π/2)= 2*1 = 2

This should make intuitive sense because the function r rises [due to the negative coefficient of the cos term] from (0,-1), has an amplitude of 2 [magnitude of the coefficient of the cos term], so it will rise as high as 3 [amplitude 2 from -1 [lowest r value] to the midline and another amplitude 2 to the maximum line] at (π,3)