# Determine an equation of a cosine function, given the following info: Amplitude: 3 Period: 120 V.Shift: 6 The function has a maximum at 15?

Mar 19, 2017

Finally sorted out! See the explanation.

#### Explanation:

The max/min ( amplitude) of $\cos \left(x\right)$ is +1 and -1. So if you wish to increase this to $\textcolor{red}{\pm 3}$ we have $y = \textcolor{red}{3} \cos \left(3 \left(x - 15\right)\right)$

'Shifting' the graph to the right so that $\underline{\textcolor{red}{\text{a}}}$ maximum (not 'the' maximum) is achieved by looking at the plot of $\cos \left(x\right)$ at the point $\textcolor{red}{x - 15}$ and plotting it at $x$. Hence the $y = 3 \cos \left(3 \left(\textcolor{red}{x - 15}\right)\right)$ The consequence is that the whole graph has been 'shifted' to the right by 15

'Squashing the curve is achieved by looking at a point for $\textcolor{red}{3} x \text{ using } \cos \left(x\right)$ and plotting it at $x$. Hence the $y = 3 \cos \left(\textcolor{red}{3} \left(x - 15\right)\right)$ 