Periodic Functions at a Glance

Graph y = -sin x.

First off, we use the general form y = a sin(bx) to track down the amplitude and period.

amplitude = |a| = |-1| = 1

But since a is negative, our graph will be flipped upside-down from a regular sine graph. Now for the period.

period = ^2π⁄₁ = 2π

And since there aren't any constants tacked onto the end, our midline is just y = 0.

Now let's make a table.

Apply the period of 2π to the five key angles and the amplitude of 1 to the five key points.

Plot your points, and don't forget to flip the shape.

Now enjoy a nice victory hot-fudge sundae.

Graph y = 0.5 sin x.

Again, we use the general form y = a sin(bx). Amplitude and period, where you at?

amplitude = |a| = 0.5

period = ^2π⁄₁ = 2π

There aren't any lone constants hanging around, so our midline is at y = 0.

Table time.

Bam. Plot your points.

Graph y = -2 cos x.

We've got an amplitude of |-2| = 2, and an upside-down cosine graph since a is negative. We've also got a period of 2π and a standard-issue midline at y = 0. Now let's table it up.

Plot 'em if you've got 'em.

Graph y = cos(½x).

The amplitude is just |1| = 1.

Now find the period.

Apply the period of 4π to the five key angles.

Plot your points. This time we'll extend our graph past 2π out to 4π so we can see a full cycle.

Graph y = 2cos(2x).

First we need to call up our two main dudes, the period and amplitude.

and amplitude = |2| = 2.

Apply the period of π to the five key angles and the amplitude of 2 to the five key points.

Now graph 'em, and extend another cycle out to 2π.