# Trigonometric ratios of Allied angles

Trigonometric ratios of allied angles, when the sum or difference of two angles is either zero or a multiple of $90^{0}$. For example $30^{0}$ and $60^{0}$ are allied angles because their sum is $90^{0}$.
The angles $-\Theta, 90^{0}\pm \Theta, 360^{0} \pm \theta$ etc. are angles allied to the angle $\Theta$, if $\Theta$ is measured in degrees. However , if $\Theta$ is measured in radians, then the angles allied to $\theta$ are $-\Theta, \frac{\pi}{2}\pm \Theta, \pi \pm \Theta, 2\pi\pm \theta$ etc. Using trigonometric ratios of allied angles we can find trigonometric ratios of angles of any magnitude.

## Results of trigonometric ratios of allied angles

 $sin (-\Theta) = - sin \Theta$ $cos (-\Theta) = cos \Theta$ $sin (90-\Theta) =cos \Theta$ $cos (90 -\Theta) = sin \Theta$ $sin (90 + \Theta) =cos\Theta$ $sin (90 +\Theta) = - sin \Theta$ $sin (180-\Theta) = sin \Theta$ $cos (180-\Theta) = - cos \Theta$ $sin (180 +\Theta) = - sin \Theta$ $cos (180+\Theta) = - cos \Theta$ $sin (270-\Theta) = - cos \Theta$ $cos(270-\Theta) = - sin \Theta$ $sin (270 +\Theta) = -cos \Theta$ $cos (270+\Theta) =sin \Theta$ $tan(90 -\Theta) = cot\Theta$ $cot (90 -\Theta) = tan \Theta$

• Trigonometric Functions
Trigonometric ratios or functions
Trigonometric reciprocal relationships
Quotient Trigonometric Identities
Pythagorean Trigonometric Identities
Signs of the Trigonometric ratios
All sin cos tan rule in Trigonometry