# How do you write an equation of a sine function with amplitude 3/4, period 720, no phase shift, vertical displacement 5 units down?

Jun 24, 2018

color(brown)("The equation is "y = (3/4) sin (x/2) - 5

#### Explanation:

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

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

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

$\text{Phase Shift } = - \frac{C}{B}$

$\text{Vertical Shift } = D$

$\text{Given ; Amplitude = 3/4, Period "= 720 = 4pi, " Vertical Shift } = - 5$
$A = \frac{3}{4} , \frac{2 \pi}{B} = 4 \pi \text{ or } B = \frac{1}{2} , D = - 5$

The equation is $y = \left(\frac{3}{4}\right) \sin \left(\frac{x}{2}\right) - 5$

graph{(3/4) sin(x/2) - 5 [-10, 10, -5, 5]}