Question

How do I convert the rectangular coordinates (5,7) to polar coordinates?

Answer 1

What are rectangular and polar coordinates?

Answer 2

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

Answer 3

hm?

Answer 4

(x,y)

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

Answer 5

x^2 + y^2 = r^2

Answer 6

what is r and theta

Answer 7

theta is the angle

you should have learned it by now if you are doing polar coordinates

Answer 8

Well, I'm a freshman and this is just on an academic team test, so I don't know any of it

Answer 9

ah, that's nice

Answer 10

How the hell did you draw that perfectly? mine was completely disgusting...

Answer 11

so rectangular coordinates just means cartesian coordinates?

Answer 12

yes

Answer 13

so, what next?

Answer 14

theta = arctan(y/x)
r= x/cos(theta)

Answer 15

what is arctan?

Answer 16

inverse operation of tangent

Answer 17

tan^-1 like on my calculator?

Answer 18

[INV] [TAN] on your calculator

Answer 19

probably.

Answer 20

Dont use the calculator..learn it

Answer 21

you using Google's calculator? Then yes it's tan^-1

Answer 22

no, my ti-84

Answer 23

2nd tan = tan^-1

Answer 24

I think that's labeled tan^-1 also... don't remember for sure...

Answer 25

yeah

Answer 26

so would doing arctan(7/5) give me the actual angle?

Answer 27

yes

Answer 28

can you explain to me why I use arctan please?

Answer 29

oh wait, I think i see

Answer 30

tangent is opp/adj which is 7/5 which gives you the actual tangent, and then convert it to the angle?

Answer 31

tan(theta) = opp/adj = y/x
tan^-1(tan(theta)) = tan^-1 (y/x)
theta = tan^-1(y/x)

Answer 32

yes, exactly.

Answer 33

sweet

Answer 34

and then we have our angle which is about 54.46 degrees

Answer 35

yes

Answer 36

now we need to find r which is sqrt(25+49)?

Answer 37

you can...

Answer 38

or r= x/cos(theta)
or r= y/sin(theta)

Answer 39

can you explain to me why the 3 are the same thing?

Answer 40

better to use the sqrt. it's valid for all quadrants, since r is usually reckoned positive (except in some quirky cases). ...since this is 1st quadrant you can use the 'shortcuts' I gave...

Answer 41

ok, would the way we found theta always work or are their exceptions too?

Answer 42

there*

Answer 43

Sort of... calculators give values for theta (when finding it by arctan) that are 1st or 4th quadrants...