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

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Presentation on theme: "Ch 5.5: Multiple-Angle and Product-to-Sum Formulas."— Presentation transcript:

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

2 Double Angle Formulas Half Angle Formulas The + or – depends in which quadrant the original given value exists

3 Ex: Find the sin2Ө and cos2Ө if 1. Draw a triangle 2. Find the missing piece 3. Use the formula

4 Ex: Find the triple angle formula for: 1. Rewrite the inside as a sum 2. Use the formula from 5.4 3. Replace with double angle formulas 4. Pythagorean Identity 5. Simplify

5 Ex: Use the half angle formula to find the exact value of sin(105 o ) 2. Double 105 to get the numerator 3. Plug into the half formula 1.105 exists in the II, so sine is positive! 4. 5. Simplify


7 Product-to-Sum and Sum-to-Product formulas: Ex: Use the correct formula to write the following product as a sum or difference: 1. Change using formula 2. Simplify

8 Ex: Find the exact value of 1.Change using sum-to- product formula 2. Simplify 3. Use trig to change cosines 4. Simplify

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