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.
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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