Derivation of Sine Half Angle Formula

Formula for sine half angle is derived by using the double angle formulas for sine and cosine.

We know, cos 2θ = 1 – 2 sin2 θ  …… (1)

Substitute θ as θ/2 in the equation (1)

=> cos θ = 1 – 2 sin2 (θ/2)

Solve the equation for sin θ/2

=> 2 sin2 (θ/2) = 1 – cos θ

=> sin2 (θ/2) = (1 – cos θ)/2

=> sin θ/2 = ±√((1 – cos θ) / 2)

This derives the formula for sine half angle ratio.

Read More:

Sine Half Angle Formula

Sine half angle is calculated using various formulas and there are multiple ways to prove the same. In this article, we have covered formulas related to the sine half angle, its derivation-related examples and others in detail.

Table of Content

  • Sine Trigonometric Ratio
    • Sine Half Angle (Sin θ/2) Formula
  • Derivation of Sine Half Angle Formula
  • Examples of Sine Half-Angle Formula
  • FAQs on Sine Half Angle Formula

Similar Reads

Sine Trigonometric Ratio

Sine ratio is expressed as the ratio of the opposing side’s length divided by the hypotenuse’s length. It is denoted by the abbreviation sin....

Derivation of Sine Half Angle Formula

Formula for sine half angle is derived by using the double angle formulas for sine and cosine....

Examples of Sine Half-Angle Formula

Example 1. If cos θ = 3/5, find the value of sin θ/2 using the half-angle formula....

FAQs on Sine Half Angle Formula

What is the formula for the half-angle formula sina.sinb?...