Half Angle formula

Sine of a Half Angle

\[\LARGE \sin \frac{a}{2} = \pm \sqrt{\frac{(1- \cos a)}{2}}\]

Cosine of a Half Angle

\[\LARGE \cos \frac{a}{2} = \pm \sqrt{\frac{(1+ \cos a)}{2}}\]

Tangent of a Half Angle

\[\LARGE \tan \left ( \frac{a}{2} \right ) = \frac{1 – \cos a}{\sin a} = \frac{\sin a}{1 + \cos a}\]


Solved Examples

Question 1: Find the value of Sin 30 degrees using the sine half-angle formula.

Given a=60 degreesUsing sine half angle formula,

$sin$ $\frac{a}{2}$ = $\pm$ $\sqrt{\frac{1-cos(a)}{2}}$

$sin$ $\frac{60}{2}$ = $\pm$ $\sqrt{\frac{1-cos(60)}{2}}$

$sin 30°$ = $\pm$ $\sqrt{\frac{1-\frac{1}{2}}{2}}$

$sin 30°$ = $\pm$ $\sqrt{\frac{1}{4}}$
$sin 30°$ = 0.5

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