Math Doubts

Cofunction identities

A mathematical relation of two trigonometric functions whose angles are complementary is called cofunction identity.

Introduction

Co-function identities can be called as complementary angle identities and also called as trigonometric ratios of complementary angles. There are six trigonometric ratios of complementary angle identities in trigonometry.

Remember, theta ($\theta$) and $x$ represent angle of right triangle in degrees and radians respectively. You can use any one of them as formula in trigonometry problems.

Sine cofunction identity

The sine of complementary angle is equal to cosine of angle.

In Degrees

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

In Radians

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

Cosine cofunction identity

The cosine of complementary angle is equal to sine of angle.

In Degrees

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

In Radians

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

Tan cofunction identity

The tangent of complementary angle is equal to cotangent of angle.

In Degrees

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

In Radians

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

Cot cofunction identity

The cotangent of complementary angle is equal to tangent of angle.

In Degrees

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

In Radians

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

Sec cofunction identity

The secant of complementary angle is equal to cosecant of angle.

In Degrees

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

In Radians

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

Cosecant cofunction identity

The cosecant of complementary angle is equal to secant of angle.

In Degrees

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

In Radians

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

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