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== Recovering the Double Angle Formulas== Using the sum formula and difference formulas for Sine and Cosine we can observe the following..."

2015-11-15T01:40:11Z

Created page with "<div class="noautonum">__TOC__</div> == Recovering the Double Angle Formulas== Using the sum formula and difference formulas for Sine and Cosine we can observe the following..."

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== Recovering the Double Angle Formulas==

Using the sum formula and difference formulas for Sine and Cosine we can observe the following identities:

::<math> \sin(2\theta) = 2\sin(\theta)\cos(\theta)</math>

::<math> \cos(2\theta) = \cos^2(\theta) - \sin^2(\theta)</math>

Using the Pythagorean Identities for trigonometric functions we can also see that:

::<math>\cos(2\theta) = 1 - 2\sin^2(\theta)</math>

::<math>\cos(2\theta) = 2\cos^2(\theta) - 1</math>

==Half Angle Formulas==

Using the last two double angle formulas we can now solve for the half angle formulas:

::<math> \sin(\theta) = \sqrt{\frac{1 - \cos(2\theta)}{2}}</math>

::<math> \cos(\theta) = \sqrt{\frac{1 + \cos(2\theta)}{2}}</math>

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Double Angle and Half Angle Formulas - Revision history

MathAdmin: Created page with "__TOC__ == Recovering the Double Angle Formulas== Using the sum formula and difference formulas for Sine and Cosine we can observe the following..."

MathAdmin: Created page with "
TOC
== Recovering the Double Angle Formulas== Using the sum formula and difference formulas for Sine and Cosine we can observe the following..."