Question

How do you find the amplitude, period, and shift for `y = 3sin(2x + pi/4)`?

Answer 1

It isn't too complicated.

Explanation:

The amplitude, which can be referred to as the variable `a`, is the number before your trig function (sin,cos, etc.). In this case, the amplitude is `3`, since it is before the sin.

The number after sin and before `x` is known as the variable `b`. To find the period of a sin function, just do: `(2pi)/b`.

The period for this particular problem would turn out to be `pi`, since `b` is `2` (from inside the parentheses) and `(2pi)/2` is just `pi`.

The shift is how much you move your graph left and right. If it is a positive number in the parentheses, you move the graph left. If it is negative, you move it right.

You move the graph left/right as many units as shown, in this case it is left `pi/4` units. That would determine your horizontal shift.

Hope this helped!