How can i create a sine graph that has a period of 2π and an amplitude of 3?

Hello!

The parent function of the graph of sin is y = sin(x).

Amplitude is the maximum displacement on the graph of a function.

Period is the displacement of x at which the graph of a function begins to repeat.

The period can be found by using the formula: .

Since the amplitude is 3, the graph of sin is y = 3sin(x).

Given the period 2π, we can substitute this value into the given formula, , to find B.

2π = 2π / B (multiply B to both sides)

2π · B = 2π (divide by 2π)

B = 1

Thus, the equation is y = 3sin(x). I'll post the graph as well.

9 x 8 divided by (5-3)=36

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1