Find the coordinates of the points on the curve

I've encountered the following question:

Find the coordinates of the points on the curve , where the tangent is horizontal.

My plan was to take the derivative and then try to find where x goes to infinity by taking the limit. Things quickly fell apart.

I managed to get the derivative of however when I check my work with WolframAlpha I'm told I'm wrong with . Now I can see the identity. However I see -1 and WolframAlpha is saying +1. My train of thought is . So where is my basic algebra failing me with +1?

Furthermore, is my thought process correct by thinking I need to find the limit as ?

Re: Find the coordinates of the points on the curve

Your derivative and Wolfram's agree. Note that in the numerator

Not sure why you would want to be concerned about the limit of y as x goes to infinity. Think more about the slope of the tangent line. What is the slope of a horizontal tangent line? Now that you have the derivative of the curve, what does the derivative tell you about slope?

Re: Find the coordinates of the points on the curve

I knew it was the same up until that point, I just didn't see the factor and how wolfram got there. :(

I think I see what to do now. Set the derivative to zero and solve?

Re: Find the coordinates of the points on the curve

Your graph has a min and a max point for 0<x<2Pi

Re: Find the coordinates of the points on the curve