Trig

Sage is an open source computer algebra system written in python.

The sine and cosine functions are available as sin(x) and cos(x), and plot draws them over an interval given as (x, a, b).

In class, we discussed how manipulating sin and cos accounts for different types of oscillation. Writing a sinusoid as A*sin(B*(x+C))+D separates those manipulations into four independent knobs:

• A — the amplitude, or how tall the wave is
• B — the frequency; the period is 2*pi/B
• C — the phase shift, sliding the wave left
• D — the vertical shift, raising the midline

The following code will plot sin(x) (blue) and A*sin(B*(x+C))+D (green) after the user defines A, B, C, and D. Drag the sliders and watch which feature of the graph each one controls.

Sage also knows the exact values that live on the unit circle, rather than only decimal approximations.