Half-Angle Formula

What is the use of Half-Angle Formulas?

Half-Angle formulas are used for finding trigonometric ratios of half of the standard angles such as 15°,22.5° and others. They are also used for solving complex trigonometric equations and are required in solving integrals, and differential equations.

What is Half Angle Formula for Sin?

Half-Angle formula for sin is 

sin A/2 = ±√[(1 – cos A) / 2]

Also, for any triangle with sides a, b, and c and semiperimeter be s, then

sin A/2 = √[(s – b) (s – c) / bc]

What is Half Angle Formula for Cosine?

Half-angle formula for cos is

cos A/2 = ±√[(1 + cos A)/2]

Also, for any triangle with sides a, b, and c and semiperimeter be s, then

cos (A/2) = √[ s (s – a)/bc]

What is the formula for cos θ?

For any right-angled triangle, with an angle θ the formula that is used to calculate the Cosine of the angle (θ) is 

Cos(θ) = adjacent / hypotenuse

Half Angle formulas are used to find various values of trigonometric angles such as for 15°, 75°, and others, they are also used to solve various trigonometric problems.

Several trigonometric ratios and identities help in solving problems of trigonometry. The values of trigonometric angles 0°, 30°, 45°, 60°, 90°, and 180° for sin, cos, tan, cosec, sec, and cot are determined using a trigonometry table. Half-angle formulas are widely used in mathematics, let’s learn about them in detail in this article.