Question
Give inequalities for $r$ and $ heta$ which describe the following regions in polar coordinates.(FIGURE CANNOT COPY)
Give inequalities for $r$ and $\theta$ which describe the following regions in polar coordinates. (FIGURE CANNOT COPY)
Answers
Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions.
$ 2 < r < 3 $, $ \quad 5\pi/3 \leqslant \theta \leqslant 7\pi/3 $
In this video, we're gonna go through the answer to question number 29 from chapter 11.4. So ask to sketch the region defined by the inequalities AA minus one after reminds one and two and theater between minus pilot T O Matic. Okay, so maybe it's best if we think this is the union of two different, uh, regions. So let's first look at the region. Between are between minus 10 that we could look at the region. Zero fessed up, fessed up. We'll have a look between after 102 s. So for this case are positive so we can blow out all of the Aah neck a wealthy positive Oz for which a pizza is not between high by two at my diplomatic empire by two. So we're looking on the, uh right Hopley Then our restraint zero, which is here two looks like here and here that we could do it semi circle around the origin, uh, within which ah is between zero and two, outside of which we can shade out. That's not in the region that we're interested in. So the reason that we're interested in is between these reds lines. So do the same thing for our butts with our is between minus one on zero s. So again, we're looking at a theater between minds pyrite even higher by two. But because I was negative. This is now on the left hand, half plain. So we control, uh, if that was too. And this is gonna be war, okay? No shade out everything. That's I'm not in that semi circle. So the area we're interested in is we did not read some hope. So to answer the whole question, let's get the union the union of these two regions. So we've got the first small semi circle a semi circle. Well, this is two one. Well, joining us up and then we can shade out everything that's not in those pictures. And that's the region that we're interested
In this video for us to you sketch the region defined by the inequalities. Where are between zero and two second pizza? That Peter is between minus pi my four by four. They said to plop this. We really need toe. Um, plot. That curve are is equal to two sec theater. So you are equal to second Eater. Then X is gonna be equal to was defined by cost eater. That's me too. One sec, Peter. Times cost eat, sir, But sexy. It was just one over Cost eater sequence to sew. This curve is just defined by the line acceptable to two. That's That's the line. Yeah. Was crossing the X axis at two. Okay, so yeah, ours between zero and that line theatre is between minus time. A four, which is along this line here, plus by by four was along this line here. So everything outside about try and go is not in. It's not in the region that we're interested in. So every shade out, all of the rest of the space, then what's left is the region
In this question, you're asked to graph the polar inequality to tell me t zero on rubber tree and or less plant. Consider the line y called Westport off three times x. Any point between this line on the X access has settled with zero on property. So any point in hysteria Andi in this area has settled between zero and poetry in this area. Are this positive in this area? Are his native So should I consider all this art? In your graph, Mr you have another limitation or less than two. So from this area, we only need to focus on points with or less than to consider this area. The circle is excess for precise. For for that means that any point on the circle asked stance to from prison because our is less than two from this area off only needs to focus on the cream part in this area. Are his list on too, and ties with Iran on forward. What about this area? Eso We exclude this part because here are is greater than what about this part? Can I had this far to the graph? Yes, because here are these between minus 20 So it is less than two on ties between zero and pull over tree. Because the points are between the eggs access plan. Decide What about this part? This part has the commitments. Iran Poetry on R is negative negative in this area, so it is less than to be at. Also there is not that quickly called zero antithetical took over three years also in the inequality. So we need to act this trigger. So today is equal to zero. I want to back next access and also Islam also must be that. Okay, so what about the point on this part off the circle? Yeah, depend on this part of the cycle has are equal to minus two minus two less than two. So this part working like miss line point on this line has our according to what? Our should be strictly less than toe. So we exclude this line I use. So I used the segment lying to sure that this part of the circle is not in our graph because our his s Tripolis that So this is the graph off there Any good hope You enjoy watching this video and hangs for watching
Quality for the time between the anger. Zero To order pie out of six on their all must be created coaches zero. So just ScanDisk inequality in the craft. Beer isn't to be the exorcist. This we we deserve on now arm would be quite a coach's era. That will be the magnitude and the damage in desert you part of sex. So we know this one would be the point of six here. And Dan Ah, any point inside this interval will be no pawned Arabs and buying this inequalities. So it would be on on the point. Yeah, and go to infinity any point in time here it will represent for on off the pond.