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

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**Double Angle Formulas Half Angle Formulas The + or – depends in**

which quadrant the original given value exists

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**Ex: Find the sin2Ө and cos2Ө if**

1. Draw a triangle 2. Find the missing piece 3. Use the formula

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**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

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**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

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**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

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**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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March 12, 2012 At the end of today, you will be able to use the double and half angle formulas to evaluate trig identities. Warm-up: Use the sum identities.

March 12, 2012 At the end of today, you will be able to use the double and half angle formulas to evaluate trig identities. Warm-up: Use the sum identities.

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