In Exercises 1–4, graph one period of each function.

y = 3 sin 2...

Question

In Exercises 1–4, graph one period of each function.

y = 3 sin 2x

Accepted Answer

Hey, everyone. Here we are asked to draw the graph of the function for one period. Here we are given the function Y is equal to 16, multiplied by sine of eight X. Here we are given a blank graph where along the X axis, we range from 0 to 5 pi divided by 16. And then along the Y axis, we range from the values negative 18 to positive 18. So our first step in drawing our graph is to first recall the formula for our sine function which is Y is equal to a multiplied by sine of BX. And now we just want to compare our given function with this corresponding formula to find our values for A and B. So here our value for A is 16 and then our value for B is eight. And now with our values identified, we want to find the amplitude and period of our function. So first beginning with the amplitude, we need to recall that the to find the amplitude, we just need to take the absolute value of A. Well, here we know A is 16. So we have the absolute value of 16 which is just 16. Therefore, our amplitude is 16 and now moving on, we need to recall our period is found by taking two pi divided by our value for B. So here we have B as eight. So our period is found by two pi divided by eight. And now just simplifying, we find our period is pi divided by four. So now with our period and amplitude identified, we can move on to finding points that lie on our graph. So first, we can notice that from our sine function, we have no vertical shifts in our graph. So our since it is a sine function, we will begin at the origin. So one of our points is going to be at zero and zero. And now to find our other points, we will find the peaks and the lowest points on our sine function. So that means we need to take our period and divide our period by four. And this again will result in our highest points and lowest points in our curve. So taking our period divided by four, we have pi divided by four, divided by four, which simplifies to pi divided by 16. So at every pi divided by 16, we will find our point. So that means we need to find the output of our function. Four pi divided by 16 as well as pi divided by eight. And then we will also have three pi divided by 16. And lastly pi divided by four and we go all the way up to pi divided by four since we are graphing for one period. So in putting all of these values into our function, we result in four different Y values. So we get four different points. So our first point will then be pi divided by and 16. Then our second point, we will have pi divided by eight and zero. Then we will have three pi divided by and negative 16. And lastly, we will, we will have pi divided by four and zero. So now we just want to start graphing all of our information. So we have five points to graph here starting again at the origin, we start at 00. Now we can move on to pi divided by 16 and 16. Next we have pi divided by eight and zero. Then we have three pi divided by 16 and negative 16. And lastly, we have the point pi divided by four and zero. And now the last step here after plotting our points is to draw, just draw a smooth curve that passes through all of these points. And with this, we have graphed our given sine function which again was Y is equal to 16, multiplied by sign of A X. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

In Exercises 1–4, graph one period of each function. y = 3 sin 2x

Key Concepts

Sine Function

Amplitude

Period

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