Question

find the values of x between 0 and 2pi where the tangent line to the graph of y=sinxcosx is horizontal.

Answer 1

Answer is pi/4, 3pi/4, 5pi/4, 7pi/4. Need the details?

Answer 2

Details:
Tangent lines are horizontal where derivative is 0:
0 = dy/dx = -sin^2(x) + cos^2(x) = cos(2x)
But cos(x) is 0 at x=pi/2, 3pi/2, 5pi/2, 7pi/2
so cos(2x) is 0 at x=pi/4, 3pi/4, 5pi/4, 7pi/4.
That's it.