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Trig Game Plan Date : 12/05/13

Trig Game Plan Date : 12/05/13. Applying the Sum and Difference Identities. If one of the angles A or B in the identities for cos( A + B ) and cos( A – B ) is a quadrantal angle, then the identity allows us to write the expression in terms of a single function of A or B .

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Trig Game Plan Date : 12/05/13

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  1. Trig Game Plan Date: 12/05/13

  2. Applying the Sum and Difference Identities If one of the angles A or B in the identities for cos(A + B) and cos(A–B) is a quadrantal angle, then the identity allows us to write the expression in terms of a single function of A or B.

  3. REDUCING cos (A – B) TO A FUNCTION OF A SINGLE VARIABLE We Do Write cos(180° - θ) as a trigonometric function of θ alone. sinθ

  4. REDUCING cos (A – B) You Do 2gether Write cos(90° + θ) as a trigonometric function of θ alone.

  5. FINDING cos (s + t) GIVEN INFORMATION ABOUT s AND t We Do Suppose that and both s and t are in quadrant II. Find cos(s + t). Sketch an angle s in quadrant II such that sin s = 3/5. Since sin s = y/r let y = 3 and r = 5. The Pythagorean theorem gives Since s is in quadrant II, x = –4 and

  6. FINDING cos (s + t) GIVEN INFORMATION ABOUT s AND t We Do The Pythagorean theorem gives Sketch an angle t in quadrant II such that Since let x = –12 and r = 5. Since t is in quadrant II, y = 5 and

  7. FINDING cos (s + t) GIVEN INFORMATION ABOUT s AND t We Do

  8. FINDING cos (s + t) GIVEN INFORMATION ABOUT s AND t We Do Suppose that , and both s and t are in quadrant IV. Find cos(s – t). The Pythagorean theorem gives Since s is in quadrant IV, y = –8.

  9. FINDING cos (s + t) GIVEN INFORMATION ABOUT s AND t We Do Use a Pythagorean identity to find the value of cos t.

  10. FINDING cos (s + t) GIVEN INFORMATION ABOUT s AND t We Do

  11. Note The values of cos s and sin t could also be found by using the Pythagorean identities.

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