# The function of a half angle of trigonometric

Just as there are identities to find the function values of 2*A*, 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 to write an identity for ½ A. Begin with the identity for written in terms of . Then solve for .

Also Read:

**Sine of ½ A**

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

for .

**Tangent of ½ A**

Use the identity . Let . 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 2*A*, 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.