In Exercises 1–6, determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π.

y = 1/3 sin x

Question

In Exercises 1–6, determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π.

y = 1/3 sin x

Accepted Answer

Hello, everyone. We are asked to identify the amplitude of the given function. Then we are going to graph it and its parent function Y equals the sign of X in the same Cartesian plane, we will be considering the domain between zero and two pi for both functions, our function is Y equals 1/8 the sign of X. So though it says to identify the amplitude first, I personally think it's a little easier if I graph our parent function first. So for the parent function Y equals the sign of X recall that it has a period of two pi and that it has an amplitude of one. So what my X Y chart would look like for this, it starts at 00 and then increases. So pi divided by two is my next X and that will increase to Y equaling one and then we increase when X equals four, this actually decreases back to Y equaling zero. The next section, our X value is three pi divided by two and our Y value would be negative one. And our last X value for this domain, it's gonna be two pie and that will be back to zero for Y. So I'm gonna put this on my Cartesian plane. So I start with the 0.0 for pi divided by two. I'm going up to one or pie. I'm back down to zero three, pi divided by two needs to be a negative one and two pi is back at zero. So here is the best I can do drawing a sine wave of that parent function. So now looking at our function, we have that Y equals 1/8 the sign of X. So there's nothing changing the period. So the period will still be too high. Amplitude will be found from the absolute value of A A is the value directly in front of the word sign. So the absolute value of 1/8 is 1/8. So we've identified our amplitude as 1/8. Um If it helps 1/8 is the same decimal as 0.125, it might make it a little simpler for us to graph. So I'm gonna make an X Y table for the points here. Since there is no fee shift, it will start at 00. Our X values will be exactly the same as they were in the parent function because there's nothing expanding or condensing them. So for pi divided by two, instead of having an amplitude of one, like we did in the parent function, we're going to multiply it by 1/8. So our amplitude here is 1/8. Next pi we'll go back to zero for uh for the Y value the three pi divided by two was negative one. It is now negative 1/8 because we need to use our new amplitude. And then for two pi why is zero again? So our Y axis is in a scale of 0.25. So we're gonna have to go just about in the middle of zero and 00. when we are graphing 1/8. So starting with 00, right on the origin pi divided by two, we need to be at 1/8 or 0.125. So roughly halfway between uh the zero line and the 00.25 line for pie, Y is zero three pi divided by two. We'd be at negative 1/8. So a little bit about halfway between zero and negative 00.25. And then for two pie, we're back at zero. So I'm gonna do my best to make this little sine wave. And so our red sign wave or our second one is not nearly as tall, but it is still a sine wave. Have a nice day.

In Exercises 1–6, determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π.y = 1/3 sin x

Verified video answer for a similar problem:

Key Concepts

Amplitude

Graphing Trigonometric Functions

Period of Sine Function