# What is the amplitude, period and the phase shift of y= 4 sin(theta/2)?

Dec 15, 2015

Amplitude, $A = 4$, Period , $T = \frac{2 \pi}{\frac{1}{2}} = 4 \pi$, Phase shift , $\theta = 0$

#### Explanation:

For any general sine graph of form $y = A \sin \left(B x + \theta\right)$,

$A$ is the amplitude and represents the maximum vertical displacement from the equilibrium position.
The period represents the number of units on the x-axis taken for 1 complete cycle of the graph to pass and is given by $T = \frac{2 \pi}{B}$.
$\theta$ represents the phase angle shift and is the number of units on the x-axis (or in this case on the $\theta$ axis, that the graph is displaced horizontally from the origin as intercept.

So in this case, $A = 4$, $T = \frac{2 \pi}{\frac{1}{2}} = 4 \pi$, $\theta = 0$.

Graphically :

graph{4sin(x/2) [-11.25, 11.25, -5.625, 5.625]}