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# Express the values of trigonometric functions at allied angles of an angle $x$ in terms of values of $x$.

Last updated date: 22nd Feb 2024
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Hint: In order to express the values of trigonometric functions at allied angles of an angle $x$, we must not consider the radians to express them instead we must we using the values of angles in degrees in the terms of angle $x$. We can find the values of the allied angles using the trigonometric functions.

Complete step-by-step solution:
Now let us learn about allied angles. Allied angles are nothing but two angles whose sum or difference is either zero or a multiple of right angle. The formula of allied angle depends upon the quadrant to which the angle belongs to. Allied angles are also called the co-interior angles. Allied angle values are nothing but simply expressing the relationship between zero angle and the right angle.
Now let us express the values of trigonometric functions at allied angles of an angle $x$ in terms of values of $x$.
As we know the sum is either zero or multiple of right angles.
So finding accordingly, we get the angles as-
$-{{x}^{\circ }},{{90}^{\circ }}\pm x,{{180}^{\circ }}\pm x,{{270}^{\circ }}\pm x,{{360}^{\circ }}-x$
Hence, we have found the allied angles in terms of angle $x$.

Note: We can also express the allied angles in terms of radians and with respect to $\theta$. The angles are to be properly braced as if not done correctly, we obtain a completely different value of the angle. In order to find the values of allied angles, we must have a grip on trigonometric functions thoroughly.