# The function of a half angle of trigonometric

Just as there are identities to find the function values of 2A, there are identities to find cos ½ A, sin ½ A , and tan ½ A. We often call the identities used to find the function values of half an angle half-angle formulas.

Cosine of ½ A

We can use the identity for $\cos 2\theta$ to write an identity for ½ A. Begin with the identity for $\cos 2\theta$ written in terms of $\cos \theta$. Then solve for $\cos \theta$.

Sine of ½ A

Begin with the identity for cos 2u, this time written in terms of $\sin \theta$. Then solve

for $\sin \theta$.

Tangent of ½ A

Use the identity $\tan \theta =\frac{\sin \theta}{\cos \theta}$. Let $\theta =\frac{1}{2}$. then substitute in the values of sin ½ A and cos ½ A.

When we use the identities for the function values of (A + B), (A B), and 2A, the sign of the function value is a result of the computation. When we use the identities for the function values of ½ A , the sign of the function value must be chosen according to the quadrant in which ½ A lies.

Also Read : The function of double – angle (2A) of trigonometric

For example, if A is a third-quadrant angle such that 180° < A < 270°, then 90° < ½ A < 135°. Therefore, ½ A is a second-quadrant angle. The sine value of ½ A is positive and the cosine and tangent values of ½ A are negative.

If A is a third-quadrant angle and 540° < A < 630°, then 270° < ½ A < 315°. Therefore, ½ A is a fourth-quadrant angle. The cosine value of ½ A is positive and the sine and tangent values of ½ A are negative.

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