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Sum and Difference Identities

Sum and Difference Identities. Using the sum and difference identities for sine, cosine, and tangent functions. Sum and Difference Identities for the Cosine Function. If α and β represent the measures of two angles, then the following identities hold for all values of α and β . .

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Sum and Difference Identities

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  1. Sum and Difference Identities Using the sum and difference identities for sine, cosine, and tangent functions

  2. Sum and Difference Identities for the Cosine Function • If α and β represent the measures of two angles, then the following identities hold for all values of α and β.

  3. Find cos 15⁰ from values of functions of 30⁰ and 45⁰.

  4. Find from values of functions of .

  5. Terri Cox is an electrical engineer designing a three-phase AC-generator. Three-phase generators produce three currents fo electricity at one time. They can generate more power for the amount of materials used and lead to better transmission and use of power then single-phase generators can. The three phases of the generator Ms. Cox is making are expressed as, . She must show that each phase is equal to the sum of the other two phases but opposite in sign. To do this, she will show that .

  6. Sum and Difference Identities for Sine Function • If α and β represent the measures of two angles, then the following identities hold for all values of α and β.

  7. Find sin 75⁰ from values of functions of 30⁰ and 45⁰.

  8. Find sin 15⁰ from values of functions of 30⁰ and 45⁰.

  9. Sum and Difference Identities for the Tangent Function • If α and β represent the measures of two angles, then the following identities hold for all values of α and β.

  10. Find tan 15⁰ from values of functions of 45⁰ and 30⁰

  11. Find tan 105⁰ from values of functions of 45⁰ and 60⁰

  12. Verify that

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