1.6 Trigonometric Functions

1. 1.6 Trigonometric Functions

3. Graphs of Trigonometric Functions • When we graph trigonometric functions in the coordinate plane, we usually denote the independent variable (radians) by x instead of θ .

4. Sine is an odd function because: Even and Odd Trig Functions: “Odd” functions behave like polynomials with odd exponents, in that when you change the sign of x, the sign of the y value also changes. Cosecant, tangent and cotangent are also odd, because their formulas contain the sine function. Odd functions have origin symmetry.

5. Even and Odd Trigonometric Functions • The graphs of cos x and sec x are even functions because their graphs are symmetric about the y-axis. • The graphs of sin x, csc x, tan x and cot x are odd functions.

6. Example Even and Odd Trigonometric Functions

8. Trig Identities

9. Angle Convention

10. Arc Length - Area

11. is a stretch. is a shrink. The rules for shifting, stretching, shrinking, and reflecting the graph of a function apply to trigonometric functions. Vertical stretch or shrink; reflection about x-axis Vertical shift Positive d moves up. Horizontal shift Horizontal stretch or shrink; reflection about y-axis Positive c moves left. The horizontal changes happen in the opposite direction to what you might expect.

12. is the amplitude. is the period. B A C D When we apply these rules to sine and cosine, we use some different terms. Vertical shift Horizontal shift

13. INVERSE TRIG FUNCTIONS

14. Inverse Trigonometric Functions