Hello!
Amplitude is the maximum displacement on the graph of a function.
Period is the displacement of x at which the graph of a function begins to repeat.
We can find the period of a circular function by using the formula: [tex] P = \frac{2\pi}{B} [/tex].
The amplitude is 6 because it causes the displacement of the graph to change. Therefore, the domain becomes -6 ≥ x ≥ 6.
To find the period, we use the formula [tex] P = \frac{2\pi}{B} [/tex], and we substitute the values into the equation. The value B, is 1/3.
[tex] P = \frac{2\pi}{\frac{1}{3}} [/tex]
This can be simplified into 6π.
Since the periodicity is 6π, the graph hits the x-axis at intervals of 3π and -3π, and the graph also hits the x-axis at the origin.
Therefore, the amplitude of the function is 6, the period is 6π, and the function hits the x-axis during intervals of 3π.
