# How do you write the equation of the cosine function with an amplitude of 2 and a period of 3pi/5?

Sep 17, 2016

$y = 2 \cos \left(\frac{10}{3} x\right)$

#### Explanation:

The standard form of the $\textcolor{b l u e}{\text{cosine function}}$ is

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y = a \cos \left(b x + c\right) + d} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

where amplitude = |a| and period$= \frac{2 \pi}{b}$

phase shift $= - \frac{c}{b} \text{ and " d=" vertical shift}$

here amplitude = 2 and period $= \frac{3 \pi}{5}$

$\Rightarrow b = \frac{2 \pi}{\frac{3 \pi}{5}} = 2 \cancel{\pi} \times \frac{5}{3 \cancel{\pi}} = \frac{10}{3}$

$\Rightarrow y = 2 \cos \left(\frac{10}{3} x\right) \text{ is the equation}$