Sine is an odd function sin sin \u03b8 \u03b8 Cosecant tangent and

# Sine is an odd function sin sin θ θ cosecant

• Notes
• 14

This preview shows page 5 - 10 out of 14 pages.

Sine is an odd function because: ( 29 ( 29 sin sin θ θ - = - Cosecant, tangent and cotangent are also odd, because their formulas contain the sine function. Odd functions have origin symmetry.
The rules for shifting, stretching, shrinking, and reflecting the graph of a function apply to trigonometric functions. ( 29 ( 29 y a f b x c d = + + Vertical stretch or shrink; reflection about x -axis Horizontal stretch or shrink; reflection about y -axis Horizontal shift Vertical shift Positive c moves left . Positive d moves up . The horizontal changes happen in the opposite direction to what you might expect. is a stretch . 1 a is a shrink . 1 b
When we apply these rules to sine and cosine, we use some different terms. ( 29 ( 29 2 sin f x A x C D B π = - + Horizontal shift Vertical shift is the amplitude . A is the period . B A B C D ( 29 2 1.5sin 1 2 4 y x π = - +
The sine equation is built into the TI-89 as a sinusoidal regression equation . For practice, we will find the sinusoidal equation for the tuning fork data on page 45. To save time, we will use only five points instead of all the data.
Time: .00108 .00198 .00289 .00379 .00471 Pressure: .200 .771 -.309 .480 .581 { } .00108,.00198,.00289,.00379,.00471 L1 ENTER 2nd { .00108,.00198,.00289,.00379,.00471 2nd } STO alpha L 1 ENTER { } .2,.771, .309,.48,.581 L2 ENTER - SinReg L1, L2 ENTER 2nd MATH 6