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

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Presentation transcript:

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

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

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

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

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

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