How do you use transformation to graph the sin function and determine the amplitude and period of y=3sin(1/2x)-2?

Feb 16, 2018

The amplitude is 3 and the period is $4 \setminus \pi$

Explanation:

One way to write the general form of the sine function is
$A \sin \left(B \setminus \theta + C\right) + D$

A = amplitude, so 3 in this case

B is the period and is defined as $P e r i o d = \frac{2 \setminus \pi}{B}$

So, to solve for B, $\frac{1}{2} = \frac{2 \setminus \pi}{B} \to \frac{B}{2} = 2 \setminus \pi \to B = 4 \setminus \pi$

This sine function is also translated 2 units down on the y axis.