Find the horizontal tangent line Fine the $x$-coordinate of all points on the curve $y=\sin(2x)+2\sin(x)$ at which the tangent line is horizontal. Consider the domain $x=[0,2\pi)$. There are three $x$ values.
Can you explain how to find the horizontal tangent line and vertical tangent line.
Also, $x=[0,2\pi)$ means that $0$ is not included?

Values at which there is a horizontal tangent are points where the tangent slope, or derivative, is $0$.  So we only need to solve $y'=2\cos (2x)-2\sin(2x)=0$
