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 122ab8f..a72541b 100644 --- a/education/math/MATH1060 (trig)/Double and Half Angle Identities.md +++ b/education/math/MATH1060 (trig)/Double and Half Angle Identities.md @@ -1,3 +1,7 @@ +To solve for a double or half angle identity: +1. Draw a triangle +2. Choose an identity to use +3. Substitute into formula # Double Angle Identities Sine: $$ \sin(2\theta) = 2\sin\theta\cos\theta $$ @@ -20,4 +24,10 @@ $$ \sin(\frac{\theta}{2}) = \pm\sqrt{\frac{1-\cos\theta}{2}} $$ Cosine: $$ \cos(\frac{\theta}{2}) = \pm \sqrt{\frac{1 + \cos\theta}{2}} $$ Tangent: -$$ \tan(\frac{\theta}{2}) = \pm\sqrt{\frac{1-\cos\theta}{1 + \cos\theta}} $$ \ No newline at end of file +$$ +\begin{matrix} +\tan(\dfrac{\theta}{2}) = \pm\sqrt{\dfrac{1-\cos\theta}{1 + \cos\theta}}\\ += \dfrac{\sin\theta}{1 + \cos\theta}\\ += \dfrac{1 - cos\theta}{\sin\theta} +\end{matrix} +$$ \ No newline at end of file