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
Pythagorean Identities cos2 θ + sin2 θ = 1 1 + tan2 θ = sec2 θ cot2 θ + 1 = csc2 θ
Example 1, pg. 446
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
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
Example 2, pg. 447
Simplifying using algebra with the identities Examples 3, 4, & 5; pg. 446
Solving Trigonometric Equations Use identities to simplify the equation. Set equal to zero and solve. Example 6, pg. 449
Solving Trigonometric Equations Example 7, pg. 450
Homework Pages 451, #2-16 even, 26, 34, 52, 54, 58.