# Formulas and Tables

Trigonometry# Periodicity of Trigonometric Functions

Trigonometric functions: \(\sin \alpha,\) \(\cos \alpha,\) \(\tan \alpha,\) \(\cot \alpha,\) \(\sec \alpha,\) \(\csc \alpha\)

Integers: \(n\)

- The least period of the sine function is \(2\pi\) or \(360^\circ\):

\(\sin \left( {\alpha \pm 2\pi n} \right) = \sin \alpha\) - The least period of the cosine function is \(2\pi\) or \(360^\circ\):

\(\cos \left( {\alpha \pm 2\pi n} \right) = \cos \alpha\) - The least period of the tangent function is \(\pi\) or \(180^\circ\):

\(\tan \left( {\alpha \pm \pi n} \right) = \tan \alpha\) - The least period of the cotangent function is \(\pi\) or \(180^\circ\):

\(\cot \left( {\alpha \pm \pi n} \right) = \cot \alpha\) - The least period of the secant function is \(2\pi\) or \(360^\circ\):

\(\sec \left( {\alpha \pm 2\pi n} \right) = \sec \alpha\) - The least period of the cosecant function is \(2\pi\) or \(360^\circ\):

\(\csc \left( {\alpha \pm 2\pi n} \right) = \csc \alpha\)

### Related Pages

- Definition and Graphs of Trigonometric Functions
- Basic Trigonometric Identities
- Cofunction and Reduction Identities
- Relationships between Trigonometric Functions
- Addition and Subtraction Formulas
- Double and Multiple Angle Formulas
- Half-Angle Formulas
- Sum-to-Product Identities
- Product-to-Sum Identities
- Powers of Trigonometric Functions
- Basic Trigonometric Equations
- Basic Trigonometric Inequalities
- Inverse Trigonometric Functions