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Trigonometric Identities

Trigonometric Identities. Review:. Pythagorean Identities. Pythagorean Identities. sin 2

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Trigonometric Identities

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  1. Trigonometric Identities

  2. Review:

  3. Pythagorean Identities

  4. Pythagorean Identities sin2𝜃 + cos2𝜃 = 12 tan2𝜃 + 12 = sec2𝜃 cot2𝜃 + 12 = csc2𝜃 sin2𝜃 + cos2𝜃 = 1 tan2𝜃 + 1 = sec2𝜃 cot2𝜃 + 1 = csc2𝜃

  5. Example If tan𝜃 = -8 and sin𝜃 > 0, find sin𝜃 and cos𝜃:

  6. Cofunction Identities sin(𝜃) = cos() tan(𝜃) = cot() csc(𝜃) = sec() cos(𝜃) = sin() cot(𝜃) = tan() sec(𝜃) = csc()

  7. Odd-Even Identities sin(-𝜃) = -sin(𝜃) cos(-𝜃) = -cos(𝜃) tan(-𝜃) = -tan(𝜃) csc(-𝜃) = -csc(𝜃) sec(-𝜃) = -sec(𝜃) cot(-𝜃) = -cot(𝜃)

  8. Example If tan𝜃 = 1.28, find cot(𝜃 - ):

  9. Simplifying and Rewriting Examples: Simplify csc𝜃sec𝜃-cot𝜃

  10. Simplifying and Rewriting Examples: Simplify sin2𝜃cos𝜃-sin(- 𝜃)

  11. Simplifying and Rewriting Examples: Simplify -

  12. Simplifying and Rewriting Examples: Rewrite as an expression that doesn’t include a fraction.

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