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

##### 1 Answer
May 10, 2016

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: $\frac{2 \pi}{b}$.

The period for this particular problem would turn out to be $\pi$, since $b$ is $2$ (from inside the parentheses) and $\frac{2 \pi}{2}$ 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 $\frac{\pi}{4}$ units. That would determine your horizontal shift.

Hope this helped!