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Problem 53 Hard Difficulty

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

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Top Algebra Educators
Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Alayna H.

McMaster University

Michael J.

Idaho State University

Video Transcript

So the equation we have is why is equal to co sign Squared off X And the question say that co sense where X is equal to 1/2 plus one over to co sign to Lex. So not to draw this graph. We basically need to try autograph off, uh, co sign to Lex within, um, could, you know, 1/2 awarded the shift of one. So let's start by setting up our access so forth. Thing I'm going to do is pro horizontal line at wise to 1/2. That is for the vertical shift. So that's the first thing. Next, the amplitude is 1/2. So I'm going to draw two more lines. One which is going to be 1.5 units above the previous line and the other one which would be one and 1/2 units below the previous life. So I have my, uh, three lines there. So the aptitude is 1/2 which means start line will go between y z zero advising him what next? We have coastline two x so the period would be too high, divided by two. And that's equal to pi. So on the X axis. We have pi over four. Then we have pi over two. And then we left being pi over four. And then finally we have pie. So used these points to draw the graph. So the graph starts at the point is you don't want It was through the point of pyro for 1/2 was on to the point out pi over 20 and then three pi over 41 and then finally high. What? So there is the graph for co sine squared off X over one people.

Other Schools
Top Algebra Educators
Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Alayna H.

McMaster University

Michael J.

Idaho State University