Yes. That method looks good.
You could just draw out the triangle I believe and not have to mess with a calculator, which may be what your teacher is getting at.
In reality it should be (I mentioned this before a lot).
For example for sine function,
$\displaystyle \sin x=\mbox{sgn } x \sqrt{\frac{1-\cos 2x}{2}}$
Where,
$\displaystyle \mbox{sgn } x=\left\{ \begin{array}{c} 1\mbox{ if }0+2\pi k\leq x\leq \pi+2\pi k\\ -1\mbox{ otherwise } \end{array} \right\}$