What's the answer to 4sin(theta)=3cos(theta), and how do you get there? Thanks!

There are two solutions on [0, 2pi]

One occurs at about (36.9, 2.4)  and the other at about (216.9, -2.4)

These solutions repeat on every 2pi interval

Here's the graph......https://www.desmos.com/calculator/xvemw185zj

4sin(theta)=3cos(theta)

$$\\4sin(\theta)=3cos(\theta)\\\\
\frac{sin\theta}{cos\theta}=\frac{3}{4}\\\\
tan\theta=0.75\\\\
\theta=atan(0.75)$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{0.75}}\right)} = {\mathtt{36.869\: \!897\: \!645\: \!844^{\circ}}}$$

Thanks Chris. 

Never forget that there is often more than one solution with trigonometry. :)

You would think I should have learned this lesson by now - I guess I haven't.  :))