Question

2 sin 5x +(Squareroot of 3)=0

Solve the multiple-angle equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)

Answer 1

\[2\sin 5x+\sqrt{3}=0,\sin 5x=-\frac{ \sqrt{3} }{ 2 }=-\sin \frac{ \pi }{ 3 }=\sin \left( \pi+\frac{ \pi }{ 3 } \right),\sin (2 \pi-\frac{ \pi }{ 3 }) \]
\[\sin 5x=\sin \left( 2 n \pi+\frac{ 4 \pi }{ 3 } \right),\sin \left( 2 n \pi+\frac{ 5 \pi }{ 3 } \right)\]
\[5x=\left( 2 n \pi +\frac{ 4 \pi }{ 3 } \right),\left( 2n \pi+\frac{ 5 \pi }{ 3 } \right)\]
x=?
where n is an integer.

Answer 2

\[-\pi/15 + 2\pi n /5 , 2\pi/3 + 2\pi n /5 \]

Answer 3

Is this correct?

Answer 4

And how do make the fractions stand up normally while typing the equation?

Answer 5

Thank you!