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

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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

- 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

Now, you try the proof for cos2 and tan 2.

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

- 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

- Find the exact value of

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

- The power reducing formulas play an important part in calculus.

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

- Find the exact value of cos105o.

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

Verify the identity:

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

Verify the identity:

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

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

- Write the product as a sum.

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

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

- Write the product as a sum.

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

- Prove the identity.

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

- 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

- Prove the identity.

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