Question

trigonometric function of half angle​

Answer 1

The half angle formulas.

The ones for sine and cosine take the positive or negative square root depending on the quadrant of the angle θ/2. For example, if θ/2 is an acute angle, then the positive root would be used.

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Answer 2

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Using the Pythagorean identity, sin 2 α+cos 2α=1, two additional cosine identities can be derived. The half‐angle identities for the sine and cosine are derived from two of the cosine identities described earlier. The sign of the two preceding functions depends on the quadrant in which the resulting angle is located.

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