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Pre-Calculus – Unit 2A Even and Odd Trigonometric Functions Worksheet Instructions: Use the Unit Circle for this limited test for even and odd functions to examine which trigonometric functions are odd or even. 𝒇(𝜽) sin 30° = csc 30° = tan 30° = cot 30° = sin 30° = sin 30° = sin 60° = csc 60° = tan 60° = cot 60° = sin 60° = sin 60° = 1 √3 𝒇(−𝜽) sin(−30° )= csc(−30° )= tan(−30° )= cot(−30° )= sin(−30° )= sin(−30° )= sin(−60° )= csc(−60° )= tan(−60° )= cot(−60° )= sin(−60° )= sin(−60° )= Test for Even or Odd 1 √3 −𝑓(𝜃) = 𝑓(−𝜃) 1 1 − ( )=− √3 Even or Odd? ODD √3 Tip: It is important to note: sin(θ) is related to the height (y position) on the circle cos (θ) is related to the side-to-side (x position) on the circle tan (θ) is related to the slope of the angle. By examining various angles versus (x, y) positions or slopes on the circle, it becomes apparent which functions must be odd or even. Tip: Remember, an even trigonometric function gives the same result whether the angle is positive or negative. If the resulting sign is the only change when the sign of the angle is reversed, the trig function is odd. Pre-Calculus – Unit 2A