SL 3.7—Trigonometric functions

Read amplitude, period and shifts from a trigonometric model.

In y=a sin(b(x+c))+d, |a| is amplitude, 2π/|b| period, c horizontal shift and d the midline.

Worked example

For y=3sin(2x−π)+4, amplitude=3, period=π, shift right π/2 and midline y=4.

Rewrite the inside as b(x+c) before reading the shift.

The inside coefficient changes period and horizontal shift, not vertical amplitude.

Graph family boundaries: sine and cosine have amplitude $|a|$ and period $2\pi/|b|$ (or $360^\circ/|b|$). Tangent has no amplitude, period $\pi/|b|$ (or $180^\circ/|b|$), zeros at integer multiples of its period and vertical asymptotes halfway between. A periodic model must state units, midline and the time represented by one complete period.