Eliminate $\theta$ from the following equations $x\cos \theta -y\sin \theta =a,x\sin \theta +y\cos \theta =b$

If $x=r\sin \theta .\cos \varphi ,y=r\sin \theta .\sin \varphi ,z=r\cos \theta$, show that:

$x^2+y^2+z^2=r^2$.

Find the values of the other five trignometric functions in the following

$\cos \theta =-\frac{8}{17},\pi <\theta <\frac{3\pi }{2}$

Find the values of the other five trignometric functions in the following;

$\cos \theta =-\frac{1}{2},\theta$ lies is the third quadrant