# Periodicity of Trigonometric Functions

• Angles (arguments of functions): $$\alpha$$
Trigonometric functions: $$\sin \alpha,$$ $$\cos \alpha,$$ $$\tan \alpha,$$ $$\cot \alpha,$$ $$\sec \alpha,$$ $$\csc \alpha$$
Integers: $$n$$
1. The least period of the sine function is $$2\pi$$ or $$360^\circ$$:
$$\sin \left( {\alpha \pm 2\pi n} \right) = \sin \alpha$$
2. The least period of the cosine function is $$2\pi$$ or $$360^\circ$$:
$$\cos \left( {\alpha \pm 2\pi n} \right) = \cos \alpha$$
3. The least period of the tangent function is $$\pi$$ or $$180^\circ$$:
$$\tan \left( {\alpha \pm \pi n} \right) = \tan \alpha$$
4. The least period of the cotangent function is $$\pi$$ or $$180^\circ$$:
$$\cot \left( {\alpha \pm \pi n} \right) = \cot \alpha$$
5. The least period of the secant function is $$2\pi$$ or $$360^\circ$$:
$$\sec \left( {\alpha \pm 2\pi n} \right) = \sec \alpha$$
6. The least period of the cosecant function is $$2\pi$$ or $$360^\circ$$:
$$\csc \left( {\alpha \pm 2\pi n} \right) = \csc \alpha$$