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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(105o)
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


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
Change using sum-to- product formula 2. Simplify 3. Use trig to change cosines 4. Simplify

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