Question

What are the six trigonometric identities?

Answer 1

Write the six trigonometric identities:

The following are the basic six trigonometric identities:

For a right-angled triangle $ABC$:

$\sin \left(\theta \right)=\frac{OppositeSide}{Hypotenuse}$

$\cos \left(\theta \right)=\frac{AdjacentSide}{Hypotenuse}$

$\tan \left(\theta \right)=\frac{OppositeSide}{AdjacentSide}$

$\mathrm{cosec}\left(\theta \right)=\frac{Hypotenuse}{Opposite\mathit{}Side}=\frac{1}{\sin \left(\theta \right)}$

$\sec \left(\theta \right)=\frac{Hypotenuse}{Adjacent\mathit{}Side}=\frac{1}{\cos \mathit{\left(}\mathit{\theta }\mathit{\right)}}$

$\cot \left(\theta \right)=\frac{AdjacentSide}{Opposite\mathit{}Side}=\frac{1}{\tan \mathit{\left(}\mathit{\theta }\mathit{\right)}}$

Hence, the six trigonometric identities are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.