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Mastering Trigonometry: Double-Angle & Half-Angle Formulas

Learn how to utilize double-angle and half-angle formulas in trigonometry. Find sine, cosine, and tangent of 2x, simplify trigonometric expressions, and calculate exact values with step-by-step examples.

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Mastering Trigonometry: Double-Angle & Half-Angle Formulas

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  1. Double-Angle and Half-Angle Formulas5.3

  2. Double-Angle Identities

  3. Example Find sin 2x, cos 2x and tan 2x if sin x = 5/13 and x lies in quadrant II.

  4. Power-Reducing Formulas

  5. Example • Write an equivalent expression for sin4x that does not contain powers of trigonometric functions greater than 1. Solution

  6. Half-Angle Identities

  7. Text Example Find the exact value of cos 112.5°. Solution Because 112.5° =225°/2, we use the half-angle formula for cos /2 with = 225°. What sign should we use when we apply the formula? Because 112.5° lies in quadrant II, where only the sine and cosecant are positive, cos 112.5° < 0. Thus, we use the - sign in the half-angle formula.

  8. Half-Angle Formulas for:

  9. Example • Verify the following identity: Solution

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