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Sum & Difference Formulas (5.2)

Sum & Difference Formulas (5.2). JMerrill, 2009. Formulas for. (The signs are the same). (The signs are opposite). To Use the Formulas. Make up any 2 angles from the unit circle (to plug in for A and B) that equal the angle you are trying to find. Example:

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Sum & Difference Formulas (5.2)

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  1. Sum & DifferenceFormulas (5.2) JMerrill, 2009

  2. Formulas for (The signs are the same) (The signs are opposite)

  3. To Use the Formulas • Make up any 2 angles from the unit circle (to plug in for A and B) that equal the angle you are trying to find.

  4. Example: • Sin 15o can be sin(60o-45o) or sin(45o-30o)

  5. Example • Find the exact value of sin15o • sin15o = sin(45o – 30o) = sin45ocos30o - cos45osin30o A = 45o, B = 30o

  6. Example • Find the exact value of • Cosine or sine formula? Cosine!

  7. Example • Find the exact value of • Sine or cosine formula? Sine!

  8. You Do • Find the exact value of cos 75o

  9. Last Example So, alpha is in QI, and beta is in QII

  10. Remember • We know so all we need is 5 13 4 5 3 -12

  11. Formula

  12. Tan Formulas • (Notice that the sign of the numerator is the same as the sign of the formula; the denominator is the opposite sign.)

  13. Example • Suppose and . Find Notice, they are NOT asking for the angles

  14. You Do • Suppose

  15. Example • Find the exact value of Go backwards—just like sine and cosine If they give you the right side of the equation, pick out alpha and beta and put them in the left side.

  16. You Do

  17. 5 5 4 3 -3 -4

  18. 5 5 4 3 -3 -4

  19. 5 5 4 3 -3 -4

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