Impromptu Speaking and Thinking on Your Feet
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The half-angle formula for sine is \(\sin\left(\frac{\theta}{2}\right) = \pm\sqrt{\frac{1 - \cos \theta}{2}}\). The sign depends on which quadrant \(\frac{\theta}{2}\) lies in. Similarly, for cosine: \(\cos\left(\frac{\theta}{2}\right) = \pm\sqrt{\frac{1 + \cos \theta}{2}}\).
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