# How do you find the amplitude, phase shift and period of Y = 4 Cos 7πX – 7?

Jun 29, 2016

The amplitude is always the number between the actual function. So in this case, the amplitude, or the number of units the graph moves up and down, is $4$.

$Y = 4 \cos 7 \pi X - 7$

The phase shift, or the horizontal distance the graph moves from the original parent function, is always the value after $x$, so in this case, the horizontal shift is $- 7$.

The period of a $\sin$ or $\cos$ graph is always determined by taking the value of $2 \pi$ and dividing it by the value before $x$. The period is the length of one cycle.

Period: $\frac{2 \pi}{7 \pi} = \frac{2}{7}$

The raw value before $x$, $7 \pi$ in this function, is identified as the cycle distance. This means that one cycle, or pattern of the graph, is $7 \pi$ units long.