Formulas

Trig Identities

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