Question

Find the exact value of sin 120° in simplest form with a rationaldenominator.

Answer 1

`\sin (120^o)=\sin (90+30)`
`\sin (a+b)=\sin a\cos b+\cos a\sin b`
`\begin{gathered} \sin (90+30)=(\sin 90)(\cos 30)+(\cos 90)(\sin 30) \\ \sin (90+30)=1(\frac{\sqrt[]{3}}{2})+0((1)/(2))_{} \\ \sin (90+30)=\frac{\sqrt[]{3}}{2} \\ \sin (120)=\frac{\sqrt[]{3}}{2} \end{gathered}`