Thread: Sinusoidal Characteristics

I am having difficulty with this function:

y = -2sin (2 ((t+1)/3)

I know to find the period I need to divide 360 degrees by the absolute value of b, but I can't figure out how to factor the equation properly to find the correct value of b.

I thought I could multiply both the 2, and the (t+1)/3 by 3 to eliminate the fraction, but that doesn't seem to be right.

I think I'm probably missing something fairly obvious... the other questions have been so easy!

I would multiply out the argument of the sin function. If you're trying to find the period, you can ignore the phase angle.

I'm not sure what you mean by, "multiply out the argument of the sin function."

I mean,

2 ((t+1)/3) = 2t/3 + 2/3.

I don't mean using the sum of angles formula.

Okay, I see what you're talking about. That works perfectly to find the period, great!

I am able to find the period, amplitude, max value, min value, range, domain, and vertical displacement from that, but am not sure how to find the horizontal shift then...

Would it be one unit to the right?
(t+1)/3 = (t-(-1))/3

Does the 3 impact it at all? I'm a little confused on that...

You're on the right track. Think of horizontal shifting this way: suppose I have a function, x^2. It's zero when x = 0, right? Now suppose I shift it horizontally. That always looks like replacing the x with an x-a or x+a. So which is which? Well, if I replace x with x-2 in our function, then I get (x-2)^2. When is that zero? When x = 2. Evidently, then, the x-2 shifting is to the right. If I were to do x+2, then I'd have (x+2)^2, which is zero when x = -2. So that one's shifted to the left.

This is how I remember which one is which. Hope that works for you.

In answer to your question, the 3 does not impact the shifting.

Awesome, thanks so much for all of your help!!!

You're very welcome!