Question

sin (2x) =-1/2

Answer 1

cool

Answer 2

\(\bf sin (2x) =-\cfrac{1}{2}\quad \textit{take }sin^{-1}
\\ \quad \\
sin^{-1}[sin ({\color{red}{ 2x}})]=sin^{-1}\left(-\frac{1}{2}\right)\implies {\color{red}{ 2x}}=sin^{-1}\left(-\frac{1}{2}\right)\)

solve for "x"

Answer 3

It says to solve the equation on the interval 0<x<2pi

Answer 4

yes
so... what did you get for "x"?

Answer 5

\[\sin 2x=-\frac{ 1 }{ 2 }=-\sin \frac{ \pi }{6 }=\sin \left( \pi+\frac{ \pi }{6 } \right),\sin \left( 2\pi-\frac{ \pi }{ 6 } \right),\sin \left( 2\pi+\pi+\frac{ \pi }{ 6 } \right),\]
\[\sin \left( 2\pi+2\pi-\frac{ \pi }{6 } \right)\]
2x=?
x=?