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For what values of € [0, 27] does the graph ofy == € + 2cos € have a horizontal tangent? Note: Write the exact answer but not the approximate valu...

Question

For what values of € [0, 27] does the graph ofy == € + 2cos € have a horizontal tangent? Note: Write the exact answer but not the approximate value (For example write 5 but not 0.8). Your answer should be written in terms of Pi or pi or T if there is a Tr in the answer:Answer:The smaller value of € isThe larger value of € is

For what values of € [0, 27] does the graph ofy == € + 2cos € have a horizontal tangent? Note: Write the exact answer but not the approximate value (For example write 5 but not 0.8). Your answer should be written in terms of Pi or pi or T if there is a Tr in the answer: Answer: The smaller value of € is The larger value of € is



Answers

Graph the polar inequality
$0 \leq \theta \leq \frac{\pi}{3}, r<2$

I've included a graph of our rose curve here now, being that it is a rose curve, we know that our maximum value is Thea absolute value of a where our three here is a So we know that our maximum value is equal to three. Now setting are curve equal to three. This occurs where the co sign is equal to one which we know is two and pie and this will equal our angle which in this case is three data. So data is two and over three high now. They wanted us to stay within the range of zero the two pi. So here, that would be 2/3 by 4/3 pi and 6/3 spy or too high, and actually we should include zero also.

For the following problem, we are going to be looking to graph the set of points to cruz polar coordinates satisfy the equations and inequalities. So if we have articles to we know it's just going to be a radius of two, no matter what the angle is, that's going to be a circle then. However, if we're considering um From 0-2, so it's going to be zero is less than or equal to our which is less than or equal to two. Then what we end up seeing is that this will create a circle where all the points inside are filled. Then if we have our is greater than or equal to one, so we know that our is going to be greater than equal to one, then what that's gonna look like is a circle but everything outside of the circle is filled in then we'll have one is between one is less than equal to our, which is less than equal to two. So in that case we end up seeing That it's going to be a circle between Radius one and radius to so of articles one R equals two. And it'll be the space filling in between creating some sort of a disk. Then we also have different angle measurements. So for example, if we're looking at the angle measurement, zero is less than or equal to theta, which is less than equal to pi over six. And we know that it can be any radius value, but we're going to have a sector from zero to pi over six. So 0 to 30 degrees, then we have other possibilities, such as uh data equals two, pi over three. That's going to be a line where no matter what the radius is, it could be positive or negative. We see it's going to be located Um to five or 3 which would be 120°. We see the same thing with pi over three except now it's just going to be 60 degrees instead of 1 20. Um and then 11 power for over two. We're going to see a lot of the same stuff, although we're just asked to change the radius. Um So the radius kind of be all positive or negative. If it's all positive, then we can have something like this where um X is greater than or equal to zero or if it's all negative, then it would just be X's less than zero for example. And that's how we would graph all these individual graphs and we see a lot of common themes throughout them.

Would you use a calculator? And here were given. X is defined as a dream time society for the the part of why we use a comma on white culture. The Atlanta but the under thirties between zero after their far by. So it was crazy, and I would say that the best windows here we want to be X between the minus 5 to 5. And while we train the minus understand up to the value on maybe five. So that's where being window that can capture on the craft here.

In this portion would you use on a graphing calculator? So the act is defined ISS the far inside I am with you three last night. I wonder why we use a comma and why you go to that six ghosts I am with the and minus ain't. And now that these defied we dreamed a zero to the to pry and it would drive. You seem proud. We see that it looks like we have number eight here. And the basket does for this one will be X can be between the months. Phone Teoh from 4 to 15. That why I can be from honest fit into is there Oh.


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