A community for students.
Here's the question you clicked on:
 0 viewing
ilikephysics2
 2 years ago
HELP Find the area of the region that lies inside both curves r = 8sin(2theta), r = 8sin(theta)
ilikephysics2
 2 years ago
HELP Find the area of the region that lies inside both curves r = 8sin(2theta), r = 8sin(theta)

This Question is Closed

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1let me guess, third year calculus?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1It was torture for me :) let me see if I can help, I need some scratch paper though

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0ok thanks man its so tough

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1i can relate, gimmie a sec

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1have you done double integrals?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1dang, okay gotta think of how to do this using single...

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0we haven't gotten that far we are in chapter 9 with areas of regions and in curves

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1give me as much info as you can then

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0well the question is just right there lol, idk what else you want

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0we have done polar coordinates, taylor series , maclaurin series

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1okay good, you can't do this in rectangular, polar is your best, no only shot unless you want roots. it's also cleaner. I just need to remember how to do a single integral sadly. I haven't done Calc 3 in a long time

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah I hear you, I'm looking at this problem and I don't even know where to start, if you can show me step by step what you do, that would be so helpful

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1\[8\sin(2\theta)=8\sin(\theta)\] \[\sin(2\theta)=\sin(\theta)\] \[2\sin(\theta)\cos(\theta)=\sin(\theta)\] \[2\sin(\theta)\cos(\theta)\sin(\theta)=0\] \[\sin(\theta)(2\cos(\theta)1)=0\] \[\sin(\theta)=0\] and \[2\cos(\theta)1=0\] Solve for theta and these are your limits of integration.

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1Notice how I cancelled the 8 but didn't cancel the sin(theta). You never want to cancel out anything that isn't a constant since it might be a potential solution.

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1Can you pick it up from there since you've done polar coordinates? I don't know if you've done integration using polar yet or not.

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0so its 2 cos(theta) = 1, so cos(theta) = 1/2?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1But believe me, you'll need a strong grip on polar since double and triple integrals build on that. Cylindrical is like a second layer to polar and spherical...well just be strong in polar and double and triple will be easier for you

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0OK so i have sin(theta) = 0 and cos(theta) = 1/2

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1yep, and notice how both functions are even( you're in polar not rectangular) so you need to take into account the negative answer

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1what are your values for theta?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1come on, your values for theta, not sin(theta) and cos(theta). Think trig or geometry. This is calculus so if you're willing to take calc, especially calc 3, you should know how to take the inverse of a trig function.

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0I thought you meant those values though

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1theta refers to the angle. What are the angles? Stop and don't think calculus right now. Go back to your geometry or trig. How did you find an angle using trig functions like sine and cosine?

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0The circle, so wouldn't it be 30 degrees

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1351461552476:dw

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0I barely remember the unit circle

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1That is a right triangle. Forget the unit circle, focus on the triangle. Cosine of which angle will give you 1/2? What two sides do you use for cosine? dw:1351461655567:dw

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0I thought it was 30 degrees?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1Oh and use that graph for sine. It's crappy but it was the best I had. Ok, what is cosine? Think back to your geometry.

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0That is the best I could remember

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1no, no, the DEFINITION of cosine

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0like which degree or just the definition?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1forget angles, forget numbers, just the textbook definition

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1Okay, so what is A/H?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1what does it stand for?

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0adjacent over hypotenuse

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1good, now when we had \[2\cos(\theta)1=0\] how did you solve it?

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0I got cos(theta) = 1/2 by adding then dividing

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1good, now look at that triangle I drew. Do you see a 1 for the adjacent, and 2 for the hypotenuse?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1right, when you have a fraction, that's what that fraction means

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1so what angle, 30, 60, or 90, will give you cos(theta)=1/2?

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0Nope 60 degrees since its a/h which is 1/2

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1351462522741:dw

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.060 degrees will give us 1/2

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1got it! so theta is 60 degrees or pi/3

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0ok yes cause they are equivalent

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1ok, so can you do the same for\[\sin(\theta)=0\]

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1Hint: you can't do this using a triangle

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1those are your limits of integration

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1yes, but do you remember the area(not under a curve) between two curves?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1how would you integrate if I said y=x^2 and y=34x^2?

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0like Big R ^2  Little r ^2?

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0so we have 0 to pi/3 of our 2 functions?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1now you have your limits of integration (in radians). You need to figure out which is the top function and which is the bottom

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0top is 8 sin(theta) and bottom is 8sin(2theta)

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1Ok, so then you know we're missing the left part of the graph then correct? since we are only going from 0 to pi/3

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0so then we have to go from pi/3 to 0?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1Nope, don't go into negative. Use the trace on your calculator and you'll see that the graph keeps going from 0 to 2pi. A lot of graphs are like that but not all

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0so whats our final integral going to look like then?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1Remember, the independent variable here isn't x like in rectangular coordinates, the angle theta (in radians) is the independent variable. Both x and y are dependent

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1Good question. There are actually two limits I didn't want to get into yet, but since you brought it up, there are TWO solutions to both sin(theta)=0 and cos(theta)=1/2 (within the restriction that theta is from 0 to 2pi.) Without that restriction, theta would have an infinite number of solutions

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0You realize this is not a double intgreal question right?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1yup, you're going to add the two integrals, just like if you had a break in the middle of a graph

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0So integral from 0 to 2pi (8sin(theta)8sin(2theta)) + 0 to pi/3 ((8sin(theta)8sin(2theta))

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1351463619332:dw

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1notice how if you did top minus bottom( which is the x axis) you need to change your limits of integration?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1It's the same idea here, but using polar

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0it is topbottom though

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0Can you draw out what the ending integral will look like

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1true, you're right there, just that the limits(BOTH LIMITS) will change

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1351463857221:dw

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1I focused on three points, but one of those points is actually a different limit of integration. For the graph of sine, what TWO values will give you 0? That's a big hint on your limits.

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0Ok cool thanks I think I got it from here

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1I hope I didn't hold back too much, but I wanted you to think and not just give you the answers. I hope I did okay

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0it was good thanks, I still have to solve for the answer though, what was your result? Mine was 12.75516082

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1uh...do you by any chance have the answer? Just a yes or no.

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1Back of the book I mean

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0yes thats my answer, oh no its webwork

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0webwork didnt take my answer

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1and no idea what webwork is

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0what did you get 8 what?

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.18 as the final answer

roadjester
 2 years ago
Best ResponseYou've already chosen the best response.1Is that the answer in your text?

ilikephysics2
 2 years ago
Best ResponseYou've already chosen the best response.0ok but our answers are both wrong
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.