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education/math/MATH1060 (trig)/Double and Half Angle Identities.md
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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 # Double Angle Identities
Sine: Sine:
$$ \sin(2\theta) = 2\sin\theta\cos\theta $$ $$ \sin(2\theta) = 2\sin\theta\cos\theta $$
@ -20,4 +24,10 @@ $$ \sin(\frac{\theta}{2}) = \pm\sqrt{\frac{1-\cos\theta}{2}} $$
Cosine: Cosine:
$$ \cos(\frac{\theta}{2}) = \pm \sqrt{\frac{1 + \cos\theta}{2}} $$ $$ \cos(\frac{\theta}{2}) = \pm \sqrt{\frac{1 + \cos\theta}{2}} $$
Tangent: Tangent:
$$ \tan(\frac{\theta}{2}) = \pm\sqrt{\frac{1-\cos\theta}{1 + \cos\theta}} $$ $$
\begin{matrix}
\tan(\dfrac{\theta}{2}) = \pm\sqrt{\dfrac{1-\cos\theta}{1 + \cos\theta}}\\
= \dfrac{\sin\theta}{1 + \cos\theta}\\
= \dfrac{1 - cos\theta}{\sin\theta}
\end{matrix}
$$