# Whats the equation for a sine function with a period of 3/7, in radians?

Apr 14, 2018

$\textcolor{b l u e}{f \left(x\right) = \sin \left(\frac{14 \pi}{3} x\right)}$

#### Explanation:

We can express trigonometric functions in the following way:

$y = a \sin \left(b x + c\right) + d$

Where:

$\setminus \setminus \setminus \setminus \boldsymbol{a} \textcolor{w h i t e}{8888} \text{ is the amplitude}$.

$\boldsymbol{\frac{2 \pi}{b}} \textcolor{w h i t e}{8. .} \text{ is the period}$

$\boldsymbol{\frac{- c}{b}} \textcolor{w h i t e}{8. .} \text{ is the phase shift}$.

$\setminus \setminus \setminus \boldsymbol{\mathrm{dc}} o l \mathmr{and} \left(w h i t e\right) \left(8888\right) \text{ is the vertical shift}$.

Note:

$\boldsymbol{2 \pi \textcolor{w h i t e}{8} \text{is the period of } \sin \left(\theta\right)}$

We require a period of:

$\frac{3}{7}$ , so we use:

$\frac{2 \pi}{b} = \frac{3}{7}$

$b = \frac{14 \pi}{3}$

So we have:

$a = 1$

$b = \frac{14 \pi}{3}$

$c = 0$

$d = 0$

And the function is:

$\textcolor{b l u e}{f \left(x\right) = \sin \left(\frac{14 \pi}{3} x\right)}$

The graph of $f \left(x\right) = \sin \left(\frac{14 \pi}{3} x\right)$ confirms this: