Ch 5.5: Multiple-Angle and Product-to-Sum Formulas

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# Ch 5.5: Multiple-Angle and Product-to-Sum Formulas - PowerPoint PPT Presentation

Ch 5.5: Multiple-Angle and Product-to-Sum Formulas. Double Angle Formulas. Half Angle Formulas. The + or – depends in which quadrant the original given value exists. 1. Draw a triangle. 2. Find the missing piece. Ex: Find the sin2 Ө and cos2 Ө if . 3. Use the formula.

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## Ch 5.5: Multiple-Angle and Product-to-Sum Formulas

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### Ch 5.5: Multiple-Angle and Product-to-Sum Formulas

Double Angle Formulas

Half Angle Formulas

The + or – depends in

given value exists

1. Draw a triangle

2. Find the missing

piece

Ex: Find the sin2Ө and cos2Ө if

3. Use the formula

1. Rewrite the inside as a sum

2. Use the formula from 5.4

Ex: Find the triple angle formula for:

3. Replace with double angle

formulas

4. Pythagorean Identity

5. Simplify

• 105 exists in the II, so sine is positive!

2. Double 105 to get

the numerator

3. Plug into the half formula

4.

5. Simplify

Product-to-Sum and Sum-to-Product formulas: p379, p380 ***These will be provided on the test ***

Ex: Use the correct formula to write the following

product as a sum or difference:

1. Change using formula

2. Simplify

Ex: Find the exact value of

• Change using sum-to-
• product formula

2. Simplify

3. Use trig to

change cosines

4. Simplify