Solve sum for theta Is there any way to solve the following sum of trigonometric functions for theta without using a solver?
$$25\sin(\theta)-1.5\cos(\theta)=20$$

$$
25\sin\theta-1.5\cos\theta = \sqrt{25^2+1.5^2}\left( \frac{25}{\sqrt{25^2+1.5^2}}\sin\theta - \frac{1.5}{\sqrt{25^2+1.5^2}}\cos\theta  \right)
$$
$$
= \sqrt{25^2+1.5^2}(\cos\varphi\sin\theta-\sin\varphi\cos\theta) = \sqrt{25^2+1.5^2} \sin(\varphi-\theta).
$$
So you want
$$
\sin(\varphi-\theta)=\frac{20}{\sqrt{25^2+1.5^2}}.
$$
Take arcsines.
