Question

Relative to the sinusoidal axes (dotted lines) what is the equation of this sinusoid?

Answer 1

Step-by-step explanation:

We know that the function period is 3 so the b value is

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

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

So our b is 2 pi/3.

The midline is -3 and the amplitude is 2.Since this function isn't symmetric about y axis, and looks symmetric about orgin, we trig function will be Sine so we have

$2 \sin ( \frac{2\pi}{3}x ) - 3$

The function passes through 0,-3 and our function on the graph passes through 1,-3 so we shift one unit to left.

$2 \sin(\frac{2\pi}{3}(x + 1) ) - 3$