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

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

  4. 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

  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

  6. 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

  7. 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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