Question

Medal!! please help

How are trigonometric functions graphed to show the period, midline, and amplitude?

Answer 1

You've already learned the basic trig graphs. But just as you could make the basic quadratic x2, more complicated, such as –(x + 5)2 – 3, so also trig graphs can be made more complicated. We can transform and translate trig functions, just like you transformed and translated other functions in algebra.

Let's start with the basic sine function, f(t) = sin(t). This function has an amplitude of 1 because the graph goes one unit up and one unit down from the midline of the graph. This function has a period of 2π because the sine wave repeats every 2π units. The graph looks like this: