This presentation is the property of its rightful owner.
1 / 17

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

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.

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

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Presentation Transcript

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