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=\frac{7\pi}{6}$$\sin \theta=\frac{\sin 7\pi}{6}$

we need to first convert the values into degrees first

$\begin{gathered} 2\pi=360 \\ \frac{7\pi}{6}=x \\ 2\pi x=\frac{7\pi}{6}\times360 \\ 2x\times6=7\times360 \\ 12x=2520 \\ x=\frac{2520}{12} \\ x=210 \\ \theta=210^0 \end{gathered}$

now we can convert the values in degrees to surds form

$\begin{gathered} \sin 210=-\frac{1}{2} \\ \frac{\sin 7\pi}{6}=-\frac{1}{2} \end{gathered}$

now let's solve for cosine

$\begin{gathered} \cos 210=-\frac{\sqrt[]{3}}{2} \\ \frac{\cos 7\pi}{6}=-\frac{\sqrt[]{3}}{2} \end{gathered}$