Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Use a polar coordinate system to plot the point with the given polar coordinates. Then find another representation (r,0) of this point in which:
(a) r> 0, 2x <0 < 4x.
(b) r<0,0<0<2R.
(c) r> 0, -2x <0<0.

(10,pi/3)


Sagot :

Step 1: Plotting the Point

Make a polar coordinate system.

It looks like this ( look at the first photo)

Step 2: Graph the polar function

r=10.

Here since our first coordinate is 10, our radius of our point will be 10.

This basically means we will have a circle with a radius of 10. ( look at the second photo).

Step 3: Look for the angle pi/3,

So that how u graph polar coordinates.

Next, a polar form can have multiple representations.

a. Here we want a radius of to be positve, so our r will stay 10.

We want our angle to lie between 2 pi and 4 pi.

So we just add 2 pi to pi/3.

[tex] \frac{\pi}{3} + 2\pi = \frac{\pi}{3} + \frac{6\pi}{3} = \frac{7\pi}{3} [/tex]

So another angle is

[tex](10, \frac{7\pi}{3} )[/tex]

B. We want r to be negative so

[tex]10( - 1) = - 10[/tex]

And we want our angle to be in between 0 and 2 pi. so we add pi to our angle.

[tex] \frac{\pi}{3} + \pi = \frac{\pi}{3} + \frac{3\pi}{3} = \frac{4\pi}{3} [/tex]

So our new representation is

[tex]( - 10, \frac{4\pi}{3} )[/tex]

C. Finally, we want our r to be positvr and our angle to be negative and in between -2pi and 0.

So we just subtract 2 pi.

[tex] \frac{\pi}{3} - 2\pi = \frac{\pi}{3} - \frac{6\pi}{3} = - \frac{5\pi}{3} [/tex]

So our new representation is

[tex](10, - \frac{5\pi}{3}) [/tex]

View image algebraic12
View image algebraic12
View image algebraic12