# How do you graph #y=1/4sin(2x+2pi)#?

##### 1 Answer

#### Answer:

Calculate the period from

#### Explanation:

The general form is

Period (radians in a cycle) =

What we'll need here is the period. Since the period is

The reason we divided by four is so that we can reach all "four corners": the midline, the highest point, the midline again, and then the lowest point. Values in between them could later be estimated.

Shifting by a full cycle, regardless of the direction, does not affect the graph, so the phase shift could also just be

Now input each angle into the function and obtain the results:

Now that we have these, let's plot them! It should look something like this:

graph{((x - 0)^2 + (y - 0)^2 - (0.05)^2)((x - pi/4)^2 + (y - 1/4)^2 - (0.05)^2)((x - pi/2)^2 + (y - 0)^2 - 0.05^2)((x - (3pi)/4)^2 + (y + 1/4)^2 - 0.05^2)((x - pi)^2 + (y - 0)^2 - 0.05^2) = 0 [-1.421, 3.882, -1.302, 1.35]}

Now estimate the graph:

graph{((x - 0)^2 + (y - 0)^2 - 0.05^2)((x - pi/4)^2 + (y - 1/4)^2 - 0.05^2)((x - pi/2)^2 + (y - 0)^2 - 0.05^2)((x - 3pi/4)^2 + (y + 1/4)^2 - 0.05^2)((x - pi)^2 + (y - 0)^2 - 0.05^2)(y - 1/4 sin(2x)) = 0 [-0.305, 4.764, -1.144, 1.39]}

And continue the cycle, both forwards and backwards!

graph{1/4 sin(2x)}

There you have it!