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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
Trigonometric functions in different quadrants


11th grade math

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