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Basic Identities Involving Sines , Cosines, and Tangents

Basic Identities Involving Sines , Cosines, and Tangents. Lesson 4.4. Pythagorean Identity. sin 2 x + cos 2 x = 1 Opposites Theorem, for all θ ,(flip over x-axis) Cos (- θ ) = cos ( θ ) Sin (- θ ) = - sin ( θ ) Tan (- θ ) = - tan( θ ). Supplements Theorem.

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Basic Identities Involving Sines , Cosines, and Tangents

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  1. Basic Identities Involving Sines, Cosines, and Tangents Lesson 4.4

  2. Pythagorean Identity • sin2 x + cos2 x = 1 Opposites Theorem, for all θ,(flip over x-axis) Cos (- θ) = cos (θ) Sin (- θ) = - sin (θ) Tan (- θ) = - tan(θ)

  3. Supplements Theorem • For all θ, measured in radians, flip over y Sin (π - θ) = sin θ Cos(π - θ) = -cos θ Tan(π - θ) = -tan θ Complements Theorem Sin (π/2 - θ) = cos θ Cos(π/2 - θ) = sin θ

  4. Half Turn Theorem (origin) • For all θ, measured in radians. Cos (π + θ) = -cos θ Sin(π + θ) = -sin θ tan(π + θ) = tan θ

  5. Example 1 • If sin θ = 1/3 , find cos θ • sin2 x + cos2 x = 1 • (1/3)2 +cos2x = 1 • Cos2x = 8/9

  6. Example 2 • If sin x = .681, find sin(-x) and sin (π – x). • Sin (-x) = -sin(x) = -.681 • Sin (π – x) = sin x = .681

  7. Example 3 • Using the unit circle, explain why sin (π – θ) = sin θ for all θ 150 30 200 -20

  8. Homework Pages 255 – 256 2 – 20 (omit 3, 8, 11, 16)

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