# How do you find the amplitude and period of y=4sin(144pit)?

Nov 11, 2016

4 and 1/72

#### Explanation:

The amplitude and period for y= a sin (kt) are a and $\frac{2}{k} \pi$.

Here, $a = 4 \mathmr{and} k = 144 \pi$, and so, the period

$P = \frac{2 \pi}{144 \pi} = \frac{1}{72}$.

See how it works.

$y \left(t + \frac{1}{72}\right) = 4 \sin \left(144 \pi \left(t + \frac{1}{72}\right)\right) = 4 \sin \left(144 \pi t + 2 \pi\right) = 4 \sin \left(144 \pi t\right) = y \left(t\right) .$

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