Question

hello can you help me with this plane trigonometry question please and thank you for your time for doing this

Answer 1

hello

`\theta=(7\pi)/(6)`
`\sin \theta=(\sin 7\pi)/(6)`

we need to first convert the values into degrees first

`\begin{gathered} 2\pi=360 \\ (7\pi)/(6)=x \\ 2\pi x=(7\pi)/(6)*360 \\ 2x*6=7*360 \\ 12x=2520 \\ x=(2520)/(12) \\ x=210 \\ \theta=210^0 \end{gathered}`

now we can convert the values in degrees to surds form

`\begin{gathered} \sin 210=-(1)/(2) \\ (\sin 7\pi)/(6)=-(1)/(2) \end{gathered}`

now let's solve for cosine

`\begin{gathered} \cos 210=-\frac{\sqrt[]{3}}{2} \\ (\cos 7\pi)/(6)=-\frac{\sqrt[]{3}}{2} \end{gathered}`