Today's soundtrack is Lecrae: Rehab, a solid rap album with a positive message.
So far, we've been working with functions whose periods were irrational. Today, we'll be learning about trigonometric functions with rational periods.
In yesterday's lesson, we learned that we can determine the period of a trigonometric function by using the equation p=2π/b. But what happens if b is 2π/x? Well, we know that dividing a fraction by another fraction just requires that we multiply the reciprocal. So the 2πs will cancel out, and we'll just be left with x as our period.
This leads us to a new form of our trig function equations: y = a cos 2π ([x-c/p]) + d . Note that b is absent, because its solution is built in with this form! In this form of our trigonometric function equation, the identities of our variables are as follows:
a = amplitude
c = phase shift
p = period
d = vertical displacement
Right then, that's it for today! Next time, we'll be looking at ways that we can model real-life situations using trigonometric functions!
Also, here's a prototype of my dream car that I whipped up in Photopea this evening:
