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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}$$
+
+Tan:
+$$ \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}} $$
+Tangent:
+$$