Trigonometry: Double-Angle and Half-Angle Formulas

Double-Angle Formulas

2 mm 2 mm

Half-Angle Formulas

, so

, so

Ex 1 Find using a half-angle formula.

Sol

Ex 2 Find if and is in Quadrant II.

Sol We have that , so since in Quadrant II. Therefore

.

Pr A Simplify the expression .

Pr 1 Find if .

Pr 2 Find if and .

Pr 3 Use a half-angle formula to find .

Pr 4 Simplify the expression

Pr 5 Use half-angle formulas to rewrite without using powers of trig functions.

Pr 6 Use half-angle formulas to rewrite without using powers of trig functions.

Pr 7 Find if and .

Pr 8 Find if and .

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