Math Doubts

Cofunction identities

A mathematical relation of two trigonometric functions whose angles are complementary is called a cofunction identity. It can be called as complementary angle identity.

There are six cofunction identities in trigonometry. Each cofunction identity is written in two different styles. In trigonometry, theta ($\theta$) symbol is used to represent angle in degrees and $x$ is used to represent angle in radians.

Cofunction identity of Sin function

$\sin{(90^\circ-\theta)} \,=\, \cos{\theta}$

$\sin{\Big(\dfrac{\pi}{2}-x\Big)} \,=\, \cos{x}$

Cofunction identity of Cos function

$\cos{(90^\circ-\theta)} \,=\, \sin{\theta}$

$\cos{\Big(\dfrac{\pi}{2}-x\Big)} \,=\, \sin{x}$

Cofunction identity of Tan function

$\tan{(90^\circ-\theta)} \,=\, \cot{\theta}$

$\tan{\Big(\dfrac{\pi}{2}-x\Big)} \,=\, \cot{x}$

Cofunction identity of Cot function

$\cot{(90^\circ-\theta)} \,=\, \tan{\theta}$

$\cot{\Big(\dfrac{\pi}{2}-x\Big)} \,=\, \tan{x}$

Cofunction identity of Sec function

$\sec{(90^\circ-\theta)} \,=\, \csc{\theta}$

$\sec{\Big(\dfrac{\pi}{2}-x\Big)} \,=\, \csc{x}$

Cofunction identity of Cosec function

$\csc{(90^\circ-\theta)} \,=\, \sec{\theta}$

$\csc{\Big(\dfrac{\pi}{2}-x\Big)} \,=\, \sec{x}$

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