Robert N.

# Calculus Question: Tangents on Polar Coordinate of Polar Curve r=cos(theta)+sin(theta)

How do I find the polar coordinates of the points on the polar curve r=cos(theta)+sin(theta), 0(greater than or equal to)(theta)(less than or equal to)(pi), where the tangent line is horizontal or vertical?

I know that I need to convert the coordinates to x & y and then take the derivative of the two (dy/dx) but can't seem to figure it out.

Using the chain rule I was able to figure out dx/d(theta)=2(-sin(theta))+cos^2(theta)-sin^2(theta)  and  dy/d(theta)=2cos(theta)+cos^2(theta)-sin^2(theta) but have no idea if I am on the correct path or what I need to do next. I thought about using the double angle trig identity but am not sure if it applies in this situation. It has been awhile since I had to utilize trig.

Any help would be awesome. Thank you.

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