Question

Find the values of x between 0 and pi where the tangent line to the graph of y = sin(x) cos(x) is horizontal.

Answer 1

Answer:

π/4, or 3π/4

Step-by-step explanation:

dy/dx = cos(x)*cos(x)+sin(x)*[-sin(x)]=(cosx)^2-(sinx)^2=[1-(sinx)^2]-(sinx)^2 = 1-2(sinx)^2

Tangent line is horizontal, so dy/dx = 0

1-2(sinx)^2 = 0

(sinx)^2 = 1/2

sinx = $\frac{1}{\sqrt{2}}, -\frac{1}{\sqrt{2}}$

Between 0 and pi, sinx >0

so sinx = $\frac{1}{\sqrt{2}}$

x = π/4, or 3π/4