Tangent Line and Coordinates of Trigonometric Function

[gabyoh23]

Homework Statement

There are infinitely many points on the curve y = \frac{sin x}{\sqrt{2}- cos x} at which the tangent line to this curve is horizontal. Find the x- and y-coordinates of one such point.

Homework Equations

y' = slope of the tangent line
Etc., etc.

The Attempt at a Solution

I know you have to take the derivative of the given equation, and at first, I tried using the quotient rule, but I got nowhere with that. Then I tried rationalizing the \sqrt{2}, but that didn't really get me anywhere either. I also have no idea how to find the x- and y-coordinates.

All help is greatly appreciated!

 

[Squeezebox]

Nothing needs to be done with \sqrt{2}, it is a constant. What's the derivative of a constant? (btw, \sqrt{2} is an irrational number which is why you couldn't rationalize it.)

The coordinates are the x and y-values of the function and y=f(x) so, (x,y)=(x,f(x))

 

[Tedjn]

To the OP, please show us your work in taking the derivative using the quotient rule. I did the same and got a particularly pleasing answer.

 

[gabyoh23]

I got something like \frac{1-cos^2(x)}{2-cos^2(x)}.
I'm not sure if this right at all. My prowess with the quotient rule is shoddy at best.