| Function | Domain | Properties |
|---|---|---|
| Sine | all real numbers | continuous on the interval \((-\infty ,\infty) \) |
| Cosine | all real numbers | continuous on the interval \((-\infty ,\infty) \) |
| Tangent | \(\left\{ x|x\neq\hbox{odd integer multiples of}\dfrac{\pi}{2}\right\} \) | continuous at all real numbers except odd multiples of \(\dfrac{\pi}{2}\)} |
| Cosecant | {\(x|x\neq\) integer multiples of π} | continuous at all real numbers except multiples of \(\pi\) |
| Secant | \(\left\{ x|x\neq \hbox{ odd integer multiples of}\dfrac{\pi}{2}\right\}\) | continuous at all real numbers except odd multiples of \(\dfrac{\pi}{2}\) |
| Cotangent | { \(x|x \neq\) integer multiples of π} | continuous at all real numbers except multiples of \(\pi\) |
| Inverse sine | \(-1\leq x\leq 1\) | continuous on the closed interval \([ -1,1]\) |
| Inverse cosine | \(-1\leq x\leq 1\) | continuous on the closed interval \([ -1,1]\) |
| Inverse tangent | all real numbers | continuous on the interval \((-\infty ,\infty) \) |
| Inverse cosecant | \(\vert x\vert \geq 1\) | continuous on the set \(\left(-\infty ,-1\right]\) \(\cup \) \([ 1,\infty) \) |
| Inverse secant | \(\vert x\vert \geq 1\) | continuous on the set \(\left(-\infty ,-1\right]\) \(\cup\) \([ 1,\infty)\) |
| Inverse cotangent | all real numbers | continuous on the interval \((-\infty ,\infty) \) |