For the following find the smallest positive value of $x$ for which.

$\sin \left(x-30°\right)=\sin 240°$

For the following find the smallest positive value of $x$ for which.

$\cos 2x=\cos 540°$

For the following find the smallest positive value of $x$ for which.

$\tan \left(\frac{x}{6}\right)=\tan \left(-476\right)$

Solve, giving all solutions between $0$ and $360$ degrees.

${\left(\sin x\right)}^2=\frac{1}{4}$

Solve, giving all solutions between $0$ and $360$ degrees.

$8{\left(\cos x\right)}^2-10\cos x+3=0$

Find the value of $x$.

$\frac{x}{\sin 50}=\frac{9}{\sin 38}$

Find the value of $x$.

$\frac{x}{\sin 25}=\frac{20}{\sin 100}$

Find the value of $x$.

$\frac{20.6}{\sin 50}=\frac{x}{\sin 70}$

Find the value of $x$.

$\frac{\sin x}{11.4}=\frac{\sin 63}{16.2}$