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Sum & Difference Formulas

Sum & Difference Formulas. Section 5.4. Learning Goal. I will be able to use sum and difference formulas to simplify trig expressions and solve trig equations. Exploration. Use a graphing calculator to graph y 1 = cos(x + 2) and y 2 = cos x + cos 2 in the same viewing window.

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Sum & Difference Formulas

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  1. Sum & Difference Formulas Section 5.4

  2. Learning Goal I will be able to use sum and difference formulas to simplify trig expressions and solve trig equations.

  3. Exploration • Use a graphing calculator to graph y1 = cos(x + 2) and y2 = cos x + cos 2 in the same viewing window. • What can you conclude about the graphs? • Is it true that cos (x + 2) = cos x + cos 2?

  4. Sums and Differences sin (A + B) = sin A cos B + sin B cos A sin (A – B) = sin A cos B – sin B cos A cos (A + B) = cos A cos B – sin A sin B cos (A – B) = cos A cos B + sin A sin B

  5. Simplify cos 3x cos 2x + sin 3x sin 2x = cos (3x – 2x) = cos x sin 105° cos 15° - cos 105° sin 15° = sin (105° - 15°) = sin 90° = 1

  6. Find the exact value of sin 150. sin 150 = sin (450 – 300) = sin 450 cos 300 – cos 450 sin 300

  7. Prove cos (p + x) = - cos x cos (p + x) = cos p cos x – sin p sin x = -1 cos x – 0 sin x = - cos x

  8. Find… Suppose sin a = 4/5 and sin q = 5/13 where 0 < a < 90° and 90° < q < 180 °. Find the value of cos (a + q). cos (a + q) = cos a cos q - sin a sin q = (3/5)(-12/13) - (4/5)(5/13) = -36/65 - 20/65 = -56/65

  9. Verify the identity:

  10. Solve in the interval

  11. What did I learn today?

  12. Homework P. 372 – 373 (1, 3, 5, 23, 30, 31, 39, 41, 47, 51, 55)

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