Question

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

Answer 1

Explanation:

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

`(2\pi)/(b) = 3`

`b = (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 ( (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((2\pi)/(3)(x + 1) ) - 3`