Solving trig equations

The idea

$\sin$, $\cos$ and $\tan$ repeat, so a trig equation has many solutions. Your calculator gives one; the graph or the unit circle gives the rest. $\sin x$ and $\cos x$ repeat every $360^\circ$, $\tan x$ every $180^\circ$.

1. Find the principal value with the inverse function.
2. Use symmetry: $\sin x$: $180^\circ - x$; $\cos x$: $360^\circ - x$; $\tan x$: $x + 180^\circ$.
3. For $\sin 2x$, solve for $2x$ over a doubled interval, then halve.

Watch out Find every solution in the interval, not just the calculator's one.