Find all points on r=2sin θ where the tangent line is parallel to the ray θ=π/4

Question

Find all points on r=2sin θ where the tangent line is parallel to the ray  θ=π/4

mathmale · Answer

Dear Cocoloco,

Welcome to OpenStudy!!

What an interesting question!

It's been a while since I last found the slope of a tangent line to a curve expressed in polar form.  You'll need to look up and apply that formula.  My suggestion:  once you have a formula for that slope, equate it to 1, because m=1 is the slope of the ray theta = Pi/4, right?

Another way to do this would be to convert r=2sin theta to the more familiar rectangular coordinates, find the derivative of the resulting function, and then set that deriv. = to 1.  Good luck!