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Warm Up

Warm Up. Verify the identity [tan(45 o + A)][tan(45 o - A)] = 1. Trig Game Plan Date : 12/11/13. Double-Angle Identities . We can use the cosine sum identity to derive double-angle identities for cosine. Cosine sum identity. Double-Angle Identities .

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Warm Up

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  1. Warm Up • Verify the identity • [tan(45o + A)][tan(45o - A)] = 1

  2. Trig Game Plan Date: 12/11/13

  3. Double-Angle Identities • We can use the cosine sum identity to derive double-angle identities for cosine. Cosine sum identity

  4. Double-Angle Identities • There are two alternate forms of this identity.

  5. Double-Angle Identities • We can use the sine sum identity to derive a double-angle identity for sine. Sine sum identity

  6. Double-Angle Identities • We can use the tangent sum identity to derive a double-angle identity for tangent. Tangent sum identity

  7. Double-Angle Identities

  8. FINDING FUNCTION VALUES OF 2θ GIVEN INFORMATION ABOUT θ We Do Given cosθ= 3/5 and sin θ < 0, find sin 2θ, cos 2θ, and tan 2θ. The identity for sin 2θ requires sin θ. Any of the three forms may be used.

  9. FINDING FUNCTION VALUES OF 2θ GIVEN INFORMATION ABOUT θ We Do Now find tan θ and then use the tangent double-angle identity. 24 7

  10. FINDING FUNCTION VALUES OF 2θ GIVEN INFORMATION ABOUT θ We Do Alternatively, find tan 2θ by finding the quotient of sin2θ and cos 2θ.

  11. FINDING FUNCTION VALUES OF 2θ GIVEN INFORMATION ABOUT θ You Do 2gether Given cos θ = 7/25 and sin θ > 0, find sin 2θ, cos 2θ, and tan 2θ.

  12. We Do Verify an identity. Quotient identity Double-angle identity

  13. You Do 2gether Verify an identity

  14. You Do 2gether Verify an identity

  15. We Do SIMPLIFYING EXPRESSION DOUBLE-ANGLE IDENTITIES Multiply by 1.

  16. You Do 2gether SIMPLIFYING EXPRESSION with DOUBLE-ANGLE IDENTITIES b) cos2 5 - sin2 5 a) 2 sin 0.45 cos 0.45 sin 2x = 2sin x cos x sin 2(0.45) = 2sin 0.45 cos 0.45 sin 0.9 = 2sin 0.45 cos 0.45 cos 2x = cos2 x - sin2x cos 2(5) = cos2 5 - sin2 5 cos 10 = cos2 5 - sin2 5

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