Formulas and Tables

Trigonometry

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 \(360^\circ\):
    \(\csc \left( {\alpha \pm 2\pi n} \right) = \csc \alpha\)