Question

Polar coordinates of a point are given. Find the rectangular coordinates of the point. (-5, -180°)

a. (-5,0)
b. (0,-5)
c. (0,5)
d. (5,0)

Answer 1

@freckles

Answer 2

\(y=r\cdot \sin(\theta)\)
\(x=r\cdot \cos(\theta)\)

Answer 3

You are given that:
\(r=-5\)
\(\theta = -180^\circ\)

Answer 4

So, -5x-180?

Answer 5

Sorry, I am teaching myself. I am somewhat confused. I need help.

Answer 6

This is in general:

\(y=r\cdot \sin(\theta)\)
\(x=r\cdot \cos(\theta)\)

(if you want to know why these values are what x and y are equivalent to, then let me know)

And in our case,
\(y=(-5)\cdot \sin(-180)=(-5)\cdot 0=0\)
\(x=(-5)\cdot \cos(-180)=(-5)\cdot(-1)=5\)

Answer 7

Oh okay. I see now.

Answer 8

I am writing this down.

Answer 9

The length of the base is x, and the length of the side is y.
This is (roughly) how cartesian coordinates are represented (ok?)

Answer 10

I am still here. I am writing this down.

Answer 11

And polar coordinates are represented differently:

You face the direction of \(\huge _{^\theta}\) and you walk in this direction \(\huge _{^{_r}}\) units long.

Answer 12

If you have questions about anything that I am posting, please ask....

Answer 13

as it is now I will assume you got no questions.

Answer 14

I am understanding well.

Answer 15

And based on the diagram 9above), you can see that:

\(\sin(\theta)={\rm opposite/hypotenuse}=y/r\)
\(\cos(\theta)={\rm adjacent/hypotenuse}=x/r\)

(this is simple trigonometry)

Now, multiply both sides of each equation times r.
You will get:

\(\displaystyle \color{red}{ r \times}\sin(\theta)=\color{red}{ r \times}\frac{y}{r}\)

\(\displaystyle\color{red}{ r \times}\cos(\theta)=\color{red}{ r \times}\frac{x}{r}\)

(r cancels on the right side of each of the equations)

\(\displaystyle r\sin(\theta)=y\)

\(\displaystyle r\cos(\theta)=x\)

Answer 16

Thus, knowing the angle, you can convert any polar coordinate to cartesian coordinate (just as we did in the example ` (-5, -180°)` )

Answer 17

Okay, I see.

Answer 18

I mean:
knowing the angle and the radius.

Answer 19

Are you doing calculus with polar coordinates, or this is some other course?

Answer 20

Pre-Calculus.

Answer 21

Oh, cool.
You will encounter it more in calculus, but as it is right now, good luck!

Answer 22

And if anything there are many people who are willing to help with stuff.....

Answer 23

bye