<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />

# Trigonometric Equations Using Half Angle Formulas

## Simplifying all six trigonometric functions with half a given angle.

0%
Progress
Practice Trigonometric Equations Using Half Angle Formulas
Progress
0%
Angle Identities

Feel free to modify and personalize this study guide by clicking "Customize".

.

#### Double Angle Identity

double angle identity relates the a trigonometric function of two times an argument to a set of trigonometric functions, each containing the original argument.

$\cos (\alpha + \alpha ) = \cos \alpha \cos \alpha - \sin \alpha \sin \alpha \\\cos 2 \alpha = \cos^2 \alpha - \sin^2 \alpha$

There are ways in which you can manipulate the double angle identity which causes there to be three ways you can present the double angle identity.

$\cos 2 \alpha= \cos^2 \alpha - \sin^2 \alpha \\\cos 2 \alpha = 2 \cos^2 \alpha -1 \\\cos 2 \alpha = 1 - 2 \sin^2 \alpha$

Hint: This double angle identity comes in handy when you are trying to solve proofs

.

Half Angle Identity

half angle identity relates the a trigonometric function of one half of an argument to a set of trigonometric functions, each containing the original argument.

$\sin \frac{\alpha}{2} = \sqrt{\frac{1 - \cos \alpha}{2}}$ if $\frac{\alpha}{2}$ is located in either the first or second quadrant.

$\sin \frac{\alpha}{2} = - \sqrt{\frac{1 - \cos \alpha}{2}}$ if $\frac{\alpha}{2}$ is located in the third or fourth quadrant.

$\cos \frac{\alpha}{2} = \sqrt{\frac{1 + \cos \alpha}{2}}$ if $\frac{\alpha}{2}$ is located in either the first or fourth quadrant.

$\cos \frac{\alpha}{2} = - \sqrt{\frac{1 + \cos \alpha}{2}}$ if $\frac{\alpha}{2}$ is located in either the second or fourth quadrant.

Tip: This all depends how the values of cosine and sine are negative dependig which quadrant cosine or sine lies on.