In Exercises 1–6, determine the amplitude of each function. Then ...

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 = 4 sin x

Accepted Answer

Hello, everyone. We are asked to identify the amplitude of the given function then graph it in its parent function Y equals sin X. In the same Cartesian plane, we will be considering the domain between zero and two pi. For both functions, the function we are given is Y equals 12 sine X. Though we are asked to identify the amplitude of the given function first, I am actually going to graph my parent function first. So Y equals the sign of X recall that the period of a sign function is and that our parent function would have an amplitude of one. So since we need four evenly spaced sections, I'm gonna start making my X Y table to graph the parent function. So we started at the 0.0 and then it'll increase to our amplitude of one. When X is pi divided by two. For the next section, we will have pi and then the Y value will go back down to zero. For the next section X is three pi divided by two and Y will be negative one because that's how our sine function flows. And our last X we need here is two pi and Y will be zero. So our parent function should look like this. If we point on 00, a point on two uh pi divided by two and one pi zero three pi divided by two and negative one and two pi goes back to zero. So I'm gonna do my best to connect these dots. So there's our parent function sine wave there, we have an amplitude of one for the one we were given Y equals 12 sign of X, the period is still too high. So we're going to use the same X values when we make our X Y table. And for the amplitude recall, you can find the amplitude by the absolute value of A A is the value directly in front of the word sign. So in this example, it's 12. So the absolute value of 12 is 12. So this means instead of only going up to one or down to negative one, we're gonna go up to 12 and down to negative 12. So we're gonna make our X Y table. And since I know the X's didn't change, I'm going to fill all of those in first. So zero pi divided by two, hi three pi divided by two and two pie. For the Y values, we're still gonna start at the 0.0. For pi divided by two, we are gonna increase to 12 because our amplitude is pi will still be zero three pi divided by two, we will decrease all the way down to negative 12 because of our amplitude. And then for two pie, we are back at zero. So let's point put those points on this graph so we can compare them. So 00 pi divided by two and 12 should be here. Pi N zero three pi divided by two and negative 12 looks just about there and two pi is back up at zero. So let me do my best to connect these. All right. It's a little squiggly but not bad. We did cover the domain from 0 to 2 pie including zero and two pie. And you can very clearly see that the amplitude of 12 makes for much larger waves than the amplitude of one in the parent function. 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 = 4 sin x

Key Concepts

Amplitude

Sine Function

Graphing Trigonometric Functions

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