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