Question

20 sin [2π(x-20)] +20 = 10. How do I find the solutions for x?

Answer 1

\[20\sin \left\{ 2\pi \left( x-20 \right) \right\}=10-20\]
\[\sin \left\{ 2\pi \left( x-20 \right) \right\}=\frac{ -10 }{20}=\frac{ -1 }{ 2 }=-\sin \frac{ \pi}{6 }\]
\[=\sin \left( \pi+\frac{ \pi }{6 } \right),\sin \left( 2\pi-\frac{ \pi }{ 6 } \right)\]
\[=\sin \frac{ 7\pi }{ 6},\sin \frac{ 13\pi }{ 6 }\]
\[2\pi \left( x-20 \right)=\frac{ 7\pi }{6 },\frac{ 13\pi }{6 }\]
\[x-20=\frac{ 7 }{ 12 },\frac{ 13 }{12 }\]
calculate x

Answer 2

omfg thank you