Add whole periods to obtain every solution. In the formulae below, α is a principal solution and n is any integer.
| Function | Period (degrees) | Period (radians) |
|---|---|---|
| \(\sin x\) | \(360^\circ\) | \(2\pi\) |
| \(\cos x\) | \(360^\circ\) | \(2\pi\) |
| \(\tan x\) | \(180^\circ\) | \(\pi\) |
General solutions in radians
\(\sin x=\sin\alpha:\quad x=\alpha+2\pi n\text{ or}\hspace{0.5em}x=\pi-\alpha+2\pi n\)
\(\cos x=\cos\alpha:\quad x=\pm\alpha+2\pi n\)
\(\tan x=\tan\alpha:\quad x=\alpha+\pi n\)
For degrees, replace \(2\pi\) by \(360^\circ\) and \(\pi\) by \(180^\circ\). Repeated families at extreme values are counted once.
For a finite interval, substitute suitable integers and list only the resulting angles inside it.
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