Originally Posted by
HallsofIvy Assuming you mean what stapel suggested, that is writing them in terms of $\displaystyle cos(\theta)$, $\displaystyle sin(\theta)$, then, yes. You use the sum formulas.
$\displaystyle cos(2\theta)= sin(\theta+ \theta)= cos(\theta)cos(\theta)- sin(\theta)sin(\theta)= cos^2(\theta)- sin^2(\theta)$
$\displaystyle sin(2\theta)= cos(\theta)sin(\theta)+ sin(\theta)cos(\theta)= 2 cos(\theta)sin(\theta)$
So
$\displaystyle sin(3\theta)= sin(2\theta+ \theta)= cos(2\theta)sin(\theta)+ sin(2\theta)cos(\theta)$
$\displaystyle cos(3\theta)= cos(2\theta+ \theta)= cos(2\theta)cos(\theta)- sin(2\theta)sin(\theta)$
and use the formulas above.
Similarly for
$\displaystyle cos(4\theta)= cos(3\theta+ \theta)$ and $\displaystyle sin(4\theta)= sin(3\theta+ \theta)$.