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Section 7.3 Double-Angle, Half-Angle, and Product-Sum FormulasPowerPoint Presentation

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

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

Chapter 7 – Analytic Trigonometry

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

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

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

- 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

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