Turn in #15 is due Friday, Mar.6, 2015!
This is for discussing assignments from WEEKS 10-11, including homework,
turn-in #15, in-class
work or lessons, or anything else related to the
class from these weeks. Please be sure to include your
name at the end of your post for credit. When answering a question, DO
NOT GIVE SOLUTIONS! Provide hints or explain a method that you used, but
do not give the final result. As always, RESPECT IS A MUST! Anyone
abusing this forum will be banned from future use (meaning, no extra
credit!!!).
Hey Mr.Wilson,
ReplyDeleteMe and Michael Bajorek have decided to change our physics project from doing the motion of a soccer ball after being kicked to athe motion of a spinning dreidal. Ms. Marentette said it was ok. i just wanted to run it by you before we did it. Is that an ok project topic?
-William Schwartz
Sure. Sounds like an opportunity to incorporate a polar function!
DeleteWill the equations for the special types of polar graphs be given to us on quizzes/ the AP test or will we need to memorize them?
ReplyDeleteAmanda Bachand
It will be helpful to recognize the shape from the function structure, much like knowing the shape of a parent function. On the AP you will either be given a graph with the functions or have your calculator available. See Turn In 15 for sample AP style questions. We will also do some APQ in class next week. Great question, Amanda!
DeleteDo we need to memorize the identities for the polar calculus or will they be on a formula sheet?
ReplyDelete-Julia T
No identities are provided on the AP. The three most useful trig identities (aside from Pythagorean) are those listed on today's handout.
DeleteAre we going to need to find surface area of a solid of revolution on the test retake tommorow?
ReplyDelete-Michael Bajorek
No
DeleteWhen you have two polar equations and you set them equal to each other will that always give you all the points of intersection?
ReplyDeleteThanks,
Rachel Hersch
Yes, you are forcing the r to be the same, and then solving for theta values.
DeleteWill we have a calculator when we work with polar stuff on a test?
ReplyDelete-Julia T
Polar functions will show up on both the calculator and non-calculator sections. If it is a non-calculator question a graph will most likely be provided. Sometimes a question will simply ask you to set up an integral, so the "work" will mainly be in finding the appropriate limits on the integral. You should be able to perform integrals like the ones we did in class today both by hand and with a calculator (just like the rectangular functions we studied). Be very familiar with the power reducing formulas!
DeleteGiven a polar equation, does the AP expect us to know what the function will look like without being able to use a calculator?
ReplyDeleteThanks, Jenna Weed
No, Mr. Wilson said that we will always either be given a calculator or a picture of the graph.
DeleteFor the project, when it says differential equation/IVP, do we need to show work for finding the C, or can we just use the calculator?
ReplyDelete-Gwen Fisher
You need to show the use of the initial condition, but you can use a calculator to evaluate a definite integral.
DeleteCan you clarify how we know when to split up the integral when solving for the area of a region?
ReplyDeleteThanks,
Allison Honet
First, keep in mind what a polar area is. It is not a region bounded by the x-axis anymore. It is a sector, with "sides" being lines radiating from the pole through theta values and the "edge" being the polar curve. This is helpful to remind yourself when looking to find a polar area, because the area extends from the pole, outward. Thus, if you want a "shared" area (such as #2 & 4 on the HW today) then you will have multiple integrals because the "edge" or boundary of your region is defined by separate curves for different theta values. Start with theta = 0 and start rotating through angular values (I am referring to #2) and you will see that at the point where the curves intersect the curve which defines the "edge" or boundary of our region changes. Therefore, we need a separate integral now. In the case where you just want the area between two polar curves, this can often be done with a single integral with each curve being either the inside or outside radius. See this link for help:
Deletehttp://tutorial.math.lamar.edu/Classes/CalcII/PolarArea.aspx
Similar to Julia's questions about the use of calculators, if we were given an area questions on the non-calculator section of the AP or final with two different polar graphs like a rose and a limacon, cardioid or circle which intersect at multiple points, how would we be able to see which intersections come first like on numbers 45 and 45 of the chapter ten review?
ReplyDeleteThanks,
Emma Gijsbers
Theta rotates through 0 to 2pi as usual, so in terms of which intersection is first it will be the first theta value you find.
DeleteWhen solving for the area between 2 polar curves, I understand that you subtract the area under the lower curve from the area under the upper curve. Conceptually, this notion of the formula makes sense to me. However, why do you multiply this value by one half?
ReplyDeleteRafey Rehman
It comes from the formula for finding the area of a sector. To find the area of a sector, you find the area of the circle that the sector is a part of (pi times radius squared) and then you multiply that by theta over 2pi, in order to get the area of the fraction of the circle that corresponds with the angle of your sector. The pi's end up canceling, so you are left with 1/2 in front of the integral. This same derivation applies if you are finding the area between 2 polar curves.
Delete-Safia Sayed
For problem 1c on the turn in, when do we use the value for d(theta)/dt or is that value irrelevant?
ReplyDelete- Daniel Honet
You have to take dy/dt and divide it by dy/d(theta) and that equals d(theta)/dt. You know d(theta)/dt and you know how to find dy/d(theta) so then you plug that in and solve for dy/dt
Delete~Katie Weitzel
Let me use this opportunity to say that the AP will not provide you with extra (unused) information in a problem. So, if you're given dr/d0, you will use it at some point.
DeleteThis comment has been removed by the author.
ReplyDeleteWill the polar area questions on the AP only be on the calculator portion if there's no graph already given?
ReplyDeleteI think so, from what Mr. Wilson said, we will either have a calculator or be given the picture of the graphs.
Delete-Marie S
This might have been discussed in class before, but what units (if any) are to be used for a polar problem if not given? Not sure if the AP requires "units," "units^2," etc., or none at all.
ReplyDeleteThanks,
Amira
From what i understand unless units are given in the problem you don't need to include them, but you could write units, or units^2 if you want...it's just not necessary.
DeleteIn what situations would I have to add up two separate integrals in order to find the area between two polar functions?
ReplyDeleteSarah Fried
I believe this happens when the piece of the area you're looking at is only affected by one of the curves. If nothing needs to be taken away in that section, it wouldn't make sense to subtract equations in the integral. Instead, you would have an integral using only one of the equations and add it to another piece. Also, see Mr. Wilson's response to Allison H.'s question above. ^^^
DeleteAmira
It is like when we did areas before. If you have to find the area of a region enclosed by two curves, a and b, and the upper hand function changes. Meaning that for part of the region, curve a is the upper-hand function,"above the region", and curve b lies below the region. But for another part of the region, b is the upper function and the area is bounded by curve a below. Your first integral would be for the interval, where a is the upper and b the lower function, a^2-b^2, and your second integral would be for when b is the upper curve, b^2-a^2
Delete-Marie Suehrer
Can we start commenting on other projects?
ReplyDeleteThanks,
Rachel Hersch
Sure!
DeleteOn the review sheet, there are several questions asking us to graph the polars. From what we have talked about in class I thought we would be either given a graph or a calculator. Is it possible we will be asked to graph polars on free response without calculator?
ReplyDelete-Marie Suehrer
What I stated above holds. The review sheet is trying to minimize paper use...use your calculator to see a graph if you like.
DeleteMr. Wilson will you be posting the solutions to the final exam review?
ReplyDeleteNo.
DeleteWould I need a calculator to decide whether to use the integral -pi/6 to 7pi/6 versus 7pi/6 to 11pi/6? Or can this be decided just from a graph on paper? If so, how?
ReplyDeleteThanks,
Julia Berthel
You should be able to analyze a polar curve as I've shown in class, with and without a calculator.
DeleteWill there be an answer key for the final exam review?
ReplyDeleteAmanda Bachand
The answers for the first 5 questions of the polar review are at the bottom of the page.
Delete-Julia Dickerson
On #1 on the Polar Calculus section on the final exam review, how do you figure out which point comes first for the interval?
ReplyDelete-Julia Dickerson
I don't have a copy with me, so I'm not sure of the specifics of the question. In general, try analyzing the polar curve by plugging in 0 for theta and determining which direction the curve rotates from there.
DeleteWhen are the comments on other people's projects due?
ReplyDeleteThanks!
Laura G
Friday, midnight. I can extend the deadline through Sunday if need be. Grades are due Monday.
DeleteWhen do you add a period to the solved theta values when solving a polar equation?
ReplyDeleteRafey
Whenever you have a coefficient in front of theta inside the trig function. For example, sin(3theta).
Delete-Safia Sayed