# How do you write the equation of a sin function: amplitude=6 period=pi phase shift= 0 vert. shift= -3/2?

Jun 26, 2018

color(blue)("Hence the equation is " y = 6 sin (2 x ) - 3/2

#### Explanation:

$\text{Standard form of a sine function is } y = A \sin \left(B x - C\right) + D$

$A m p l i t u \mathrm{de} = | A | = 6$

$\text{Period } = \frac{2 \pi}{|} B | = \pi , | B | = \frac{2 \pi}{\pi} = 2$

$\text{Phase Shift " = -C / B = 0 } \mathmr{and} ' C = 0$

$\text{Vertical Shift } = d = - \frac{3}{2}$

color(blue)("Hence the equation is " y = 6 sin (2 x ) - 3/2

graph{6 sin (2x) - 3/2 [-10, 10, -5, 5]}