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Chapter 7 – Analytic Trigonometry. Section 7.3 Double-Angle, Half-Angle, and Product-Sum Formulas. Double Angle Formulas. The double-angle formulas allow us to find the values of the trigonometric functions at 2 x from their values at x. Proofs of Double Angle Formulas.

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## Section 7.3 Double-Angle, Half-Angle, and Product-Sum Formulas

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**Chapter 7 – Analytic Trigonometry**Section 7.3 Double-Angle, Half-Angle, and Product-Sum Formulas 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Double Angle Formulas**• The double-angle formulas allow us to find the values of the trigonometric functions at 2x from their values at x. 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Proofs of Double Angle Formulas**Now, you try the proof for cos2 and tan 2. 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Example**• If and lies in quadrant II, find the exact value of each of the following: 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Example**• Find the exact value of 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Power Reducing Formulas**• The power reducing formulas play an important part in calculus. 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Half Angle Formulas**• NOTE: The choice of the + or – sign depends on the quadrant in which u/2 lies. 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Example**• Find the exact value of cos105o. 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Example**Verify the identity: 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Example**Verify the identity: 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Product-to-Sum Formulas**7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Examples – pg. 515**• Write the product as a sum. 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Sum-to-Product Formulas**7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Examples – pg. 515**• Write the product as a sum. 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Example – pg. 515**• Prove the identity. 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**Example**• Write an equivalent expression for cos4x that does not contain powers of trigonometric functions greater than 1. 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas**More Examples**• Prove the identity. 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas

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