diff --git a/education/math/MATH1060 (trig)/Double and Half Angle Identities.md b/education/math/MATH1060 (trig)/Double and Half Angle Identities.md index c89557f..c92bc46 100644 --- a/education/math/MATH1060 (trig)/Double and Half Angle Identities.md +++ b/education/math/MATH1060 (trig)/Double and Half Angle Identities.md @@ -1,5 +1,7 @@ # Double Angle Identities +Sine: $$ \sin(2\theta) = 2\sin\theta\cos\theta $$ +Cosine: $$ \begin{matrix} \cos(2\theta) = \cos^2\theta - \sin^2\theta\\ @@ -7,4 +9,15 @@ $$ = 2cos^2\theta - 1\\ \end{matrix} $$ -$$ \tan(2\theta) = \dfrac{2\tan\theta}{1-\tan^2\theta}$$ \ No newline at end of file + +Tan: +$$ \tan(2\theta) = \dfrac{2\tan\theta}{1-\tan^2\theta}$$ + +## Half Angle Identities +Whether the output is positive or negative depends on what quadrant the output is in. +Sine: +$$ \sin(\frac{\theta}{2}) = \pm\sqrt{\frac{1-\cos\theta}{2}} $$ +Cosine: +$$ \cos(\frac{\theta}{2}) = \pm \sqrt{\frac{1 + \cos\theta}{2}} $$ +Tangent: +$$ \ No newline at end of file