Well this weekend I was pretty bummed because I knew I had a lot of math to do. I was even more bummed when I actually started working because those take home test were uber hard but now that I’m actually finished I feel ok about the test tomorrow. Anyways:
Well this week we particularly stayed on graphs and I feel like I know it but then I get it wrong. The graphs I don’t have trouble with or the ones that are on the study guide.
But I don’t really understand how to get the points of inflection and intervals when you have a problem with lets say sin or cos in it. Working the problem is not the problem; its just when I get to the part when your getting the possible points of inflection that messes me up because I don’t really remember or understand when and how do the part in the problem when you use the quadrants of the graph to find the points of inflection. So if anybody understands what I’m asking and wouldn’t mind explain it to me that would really help. I know my quadrants for like sin, cos, and etc. but its just when you get like 30 and you have to subtract 360 I get all lost.
But other than when I’m dealing with a problem like that I’m pretty sure I grasp the first derivative test and the second derivative test.
About feeling ok on that test tomorrow I LIED!!! :o
GOOD LUCK. :dodgy:
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Sin is positive on the top 2 quadrants
ReplyDeleteCos is positive on the right 2 quadrants
Tan is positive on the top right and bottom left
if you have sin(30)and you are looking for the other one, since 30 is already in the top right quadrant the way to get it to the other is make it negative and add 180 to get to the other quadrant you need to get to.
If you have cos(30)and looking for the other one, 30 is already in the right quadrant so the way to get it to the other which is the bottom right one make it negative and the way to get rid of the negative is just add 360 and your done.
And finally if you have tan(30)the way to find the other since it is already in the top right quadrant all you do is add 180.
hope this helps
To find possible points of inflection, you have to take the second derivative then set it equal to zero and solve for x. The point(s) you come up with are possible points of inflection. Then you have to set up intervals and check to see if there is a change in concavity at those points. If there is, then those are your points of inflection.
ReplyDeleteIf you are trying to find where cos is positive which is going from quadrant 1 to 4 that is when you have to make the angle in quadrant 1 negative which puts you in quadrant 4 and add 360 because a angle cannot be negative.
If you need to find points of inflection, know that it is pertaining to the second derivative. First take the second derivative and then set it equal to zero. Then solve for x, giving you possible points of inflection. After you have to set up intervals using these points to see if there is a change in concavity on any of those points. If there is a change in concavity, that means there is a point of inflection at that particular point :)
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