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1
Trigonometric Identities (Lesson 5-1)
sin θ = 1 / csc θ cos θ = 1 / sec θ tan θ = 1 / cot θ csc θ = 1 / sin θ sec θ = 1 / cos θ cot θ = 1 / tan θ tan θ = sin θ / cos θ cot θ = cos θ / sin θ
2
Pythagorean Identities
cos2 θ + sin2 θ = tan2 θ = sec2 θ cot2 θ + 1 = csc2 θ
3
Example 1, pg. 446
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Cofunction Identities
sin (π/2 – θ) = cos θ cos (π/2 – θ) = sin θ tan (π/2 – θ) = cot θ cot (π/2 – θ) = tan θ csc (π/2 – θ) = sec θ sec (π/2 – θ) = csc θ
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Odd – Even Identities sin (-x) = - sin x cos (-x) = cos x tan (-x) = - tan x csc (-x) = - csc x sec (-x) = sec x cot (-x) = - cot x
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Example 2, pg. 447
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Simplifying using algebra with the identities
Examples 3, 4, & 5; pg. 446
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Solving Trigonometric Equations
Use identities to simplify the equation. Set equal to zero and solve. Example 6, pg. 449
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Solving Trigonometric Equations
Example 7, pg. 450
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Homework Pages 451, #2-16 even, 26, 34, 52, 54, 58.
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