Question

What is the exact value of sin 165°?without using a calculator

Answer 1

\[\sin 165=\sin \left( 120+45 \right)=\sin 120\cos 45+\cos 120\sin 45\]
\[\sin 120=\sin \left( 180-60 \right)=\sin 60=\frac{ \sqrt{3} }{2 }\]
\[\cos 120=\cos \left( 180-60 \right)=-\cos 60=-\frac{ 1 }{ 2 }\]
\[\sin 45=\cos 45=\frac{ 1 }{ \sqrt{2} }\]
plug the values and find the solution.