Find Horizontal Tangent Pts for y = 9sin(x)cos(x)

[Physics1]

Homework Statement

y = 9sin(x)cos(x)

Find all points where tangent line is horizontal.

The Attempt at a Solution

I get y' = 9cos^2x - 9sin^2X

I plug in zero for the slope and get 9 but I'm stumped after that. How can I get all the horizontal tangent line points?

 

[cristo]

Homework Statement

y = 9sin(x)cos(x)

Find all points where tangent line is horizontal.

The Attempt at a Solution

I get y' = 9cos^2x - 9sin^2x
I plug in zero for the slope and get 9 but I'm stumped after that.

How?

How can I get all the horizontal tangent line points?

You do exactly what you say to do; that is, find the points where the derivative of the graph is zero. It boils down to solving cos^2x-sin^2x=0. Can you do this?

[Hint: cos^2x=1-sin^2x]