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Problem 52 Hard Difficulty

In Section 9.2 you'll see the identity $\sin ^{2} x=\frac{1}{2}-\frac{1}{2} \cos 2 x$. Use this identity to graph the function $y=\sin ^{2} x$ for one period.

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Top Algebra Educators
Catherine R.

Missouri State University

Alayna H.

McMaster University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Video Transcript

so we need to draw the graph off. Why is he called to sine squared off X? And the question says we that sine squared off X can also be written as 1/2 minus one over to co sign off two weeks. So basically, we need to draw the graph. Of course, I'm two X, with an aptitude of 1/2 and a vertical shift off 1/2. So let's ah, start by setting up our access. So we have our basic X and y axes. Secondly, since there's a vertical shift off 1/2 therefore, to start things off with, just draw a horizontal line at why is equal to about half next. We know that the amplitude is 1/2 so we draw a line 1/2 minutes above this, which would be at one and another line at 1/2 minutes below it. So these are the values or while between which are graph would be plotted. So we have said next because it says coastline two X there for the period would be to pie divided by two, which is equal to pi. So here we have pipe or four. Next, I over to next. We have three pi over four and then the F pie. So those are extract use that we would need. Now, this is a negative coasting to X graph. So it's gonna start here at the origin and then go through this point Piper for 1/2 and then go on to if I were to one and then three pi over 4 1/2 and then finally he Hi is you. So that would be the graph that wouldn't draw for this question.

Other Schools
Top Algebra Educators
Catherine R.

Missouri State University

Alayna H.

McMaster University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University