1. ## period and amplitude

Find the amplitude and period of:

y=5sin(2x) + 4sin(7x)

i got 8.886 for the amplitude

how do i get the period?

thanks

2. Originally Posted by Mr_Green
Find the amplitude and period of:

y=5sin(2x) + 4sin(7x)

i got 8.886 for the amplitude

how do i get the period?

thanks
Hello,

you have to consider 2 different periods:
$p_1 = \frac{2\pi}2=\pi$ and
$p_2 =\frac{2\pi}7=\frac27 \cdot \pi$

You get the period of the combined function if the equation
$n \cdot p_1 = k \cdot p_2~, n,k~\in~\mathbb{Z}$ is true. Therefore:

$n \cdot \pi= k \cdot \frac27 \cdot \pi$
$\frac nk = \frac27$. The first possible values for n and k are:

$\frac nk ~\frac{\rightarrow}{\rightarrow}~ \frac27$. If n = 2 then $p_1 = 2\pi$ and if k = 7 then $p_2 = 2\pi$, thus the period of your function is $2\pi$