# How do you write a cosine equation with max= 21, min= 15 and period=15?

Jul 25, 2016

$x = B + 3 \cos \left(\frac{2 \pi}{15} t + E\right)$, where B and E are arbitrary constants.

#### Explanation:

The general form of cosine wave with axis parallel to t-axis, axis about which it oscillates x = B, amplitude A, period P and epoch (shift) E is

$x - B + A \cos \left(\left(\frac{2 \pi}{P}\right) t + E\right)$.

Here 2 A = maximum x - minimum x $= 21 - 15 = 6$. So, A = 3.

The period $\frac{2 \pi}{P} = 15$. So, $P = \frac{2 \pi}{15}$..

Thus, this coscine oscillation is given by

$x = B + 3 \cos \left(\frac{2 \pi}{15} t + E\right)$, where B and E are at your choice.