Question

Challenge Question:
Using polar coordinates graph r = cos(4θ) fill the region in with yellow.
Using cartesian coordinates graph x^2 + y^2 = 1/4
Using cartesian coordinates graph y = -x from .3 to 3

Answer 1

Graph the last equation in green

Answer 2

use some kind of graphing software ... for help
http://www.wolframalpha.com/input/?i=polar+plot+r+%3D+cos%284%CE%B8%29+
http://www.wolframalpha.com/input/?i=plot+x^2+%2B+y^2+%3D+1%2F4
http://www.wolframalpha.com/input/?i=plot+y+%3D+-x+from+-0.3+to+0.3

Answer 3

The first one, without color

Answer 4

They need to be graphed together.

Answer 5

Together?

Answer 6

Yup. Following the instuctions.

Answer 7

Color is actually kind of important for this. :P

Answer 8

So it's your homework?

Answer 9

Nope, it's a challenge question, you said math was boring...

Answer 10

You don't even have to send me a picture, if you can tell me what it looks like.

Answer 11

#2 is a circle with radius \(\frac 12\) and center at the origin.
#3 is a straight line passing through the origin second and fourth quadrant.

Answer 12

So?

Answer 13

What does it look like when you put it together?

Answer 14

How could we put polar and cartesian together?

Answer 15

Just draw the graphs over the top of eachother?

Answer 16

Why would we want to do that?

Answer 17

You could draw circles lightly to get a cartesian graph over a normal graph around the origin.

Answer 18

Yes yes, but why?

Answer 19

Because it looks neat?

Answer 20

lol, I thought it has some mathematical significance.

Answer 21

Nope. I'm smart enough for that kind of stuff. I appreciate normal things that look pretty, smell pretty, and feel nice. Math is abstract so I have to make it into something I can appreciate.

Answer 22

Anyways, it makes a picture of a daisy.

Answer 23

Math is extremely important for animation though, 3D rendering is all very mathy.