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6.1 Sum & Difference Identities

6.1 Sum & Difference Identities. All the identities we learned in Ch 4 were with one angle We have identities that involve more than 1 angle! Question: Can we do this? sin 90° = sin (60° + 30°) Let’s check…. sin 90° = 1 So…. NO!. = sin 60° + sin 30°. sin 60° + sin 30° =.

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6.1 Sum & Difference Identities

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  1. 6.1 Sum & Difference Identities

  2. All the identities we learned in Ch 4 were with one angle We have identities that involve more than 1 angle! Question: Can we do this? sin 90° = sin (60° + 30°) Let’s check…. sin 90° = 1 So…. NO! = sin 60° + sin 30° sin 60° + sin 30° = There must be rules! Difference Identity for Cosine Sum Identity for Cosine Difference Identity for Sine Sum Identity for Sine

  3. We can use “famous angle” values to calculate other angles. Think of what you can add or subtract to get the angle Often deal with denominators of 12. Ex 1) Find the exact value of: a) b)

  4. Ex 2) Find the exact value of sin ( + ) given that : : 13 12 4   –5 –3 5

  5. Difference Identity for Tangent Sum Identity for Tangent

  6. Ex 3) A video security monitor is to be mounted 10 feet above the floor on the back wall of a store. It will scan through an angle θ in a vertical plane along the aisle. The aisle begins 5 feet from the back wall & is 40 feet long. Through what angle must the monitor rotate? • From Geo: exterior angle is sum of 2 remote interior angles • = θ +  • θ =  –  θ 10   5 40

  7. Let’s prove Sum & Difference Identities for tangent Put the “puzzle” pieces in the correct order. Answers: Sum: D I L A F K Diff: G B J E C H

  8. Homework #601 Pg 290 #3, 9, 13, 17, 19, 23, 27, 33, 41, 45, 47, 55, 61

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