Question

Determine two pairs of polar coordinates for the point (5, -5) with 0° ≤ θ < 360°

Answer 1

https://i.gyazo.com/1a50524381eaebcd22762fa6292443fe.png

Answer 2

hey i actually got stuck @Astrophysics

Answer 3

Hey, no worries, where did you get stuck?

Answer 4

I will just put this for a reference \[x = r \cos \theta\]\[y= r \sin \theta\]\[r^2 = x^2+y^2 \implies r = \sqrt{x^2+y^2}\], and lets go over it

Answer 5

ok so i plugged in everything...
r=sqrt(5^2 + (-5)^2)
but when i solved for theta my answer wasnt one of the options

Answer 6

r = 5sqrt(2)

Answer 7

Ok lets see, so you did \[r = \sqrt{x^2+y^2} \implies r = \sqrt{(5)^2+(-5)^2} = \sqrt{50} = 5\sqrt{2}\] so far so good?

Answer 8

yea i got that

Answer 9

Ok cool, so the angles can be quite tricky that's why I had drawn the triangle for you earlier, so here we have to use the tan ratio to find the angle

Answer 10

ok so tan(theta) = -5/5

Answer 11

???

Answer 12

Yes exactly!

Answer 13

tan(theta) = -1
from here to I inverse it?

Answer 14

Yup \[\theta = \tan^{-1}(-1)\]

Answer 15

ok give me a sec

Answer 16

7pi/4

Answer 17

Good so that is 315 degrees

Answer 18

ok so it would be 5sqrt(2),315

Answer 19

Yes, and the other you want for \[-5\sqrt{2}\]

Answer 20

Which is just 315-180

Answer 21

135

Answer 22

Bingo

Answer 23

so the answer is A?

Answer 24

Sounds good!

Answer 25

Thank you so much for the help! :)

Answer 26

Np :)

Answer 27

x is positive and y is negative
so it is below x-axis
x is positive , yis negative ,hence in fourth quadrant.

Answer 28

Yup I already had shown that in the previous post ;P

Answer 29

you mind helping me with one more? sorry. lol

Answer 30

Sure haha

Answer 31

Find all polar coordinates of point P = (2, 14°)

Answer 32

n is an integer

Answer 33

x = 1.94059
y = 0.48384

Answer 34

Ok maybe I shouldn't have wrote that just ignore it and look at what I said after

Answer 35

lol ok

Answer 36

so would it just be (2, 14 +/- 2npi) ???

Answer 37

Yes that works (2, 14 +360n) as we're using degrees

Answer 38

is that it?

Answer 39

yes or (-2, 14+90+360n)

Answer 40

wait im confused now where did the 90 come from?

Answer 41

Look at what I said twice, the polar representations

Answer 42

so all the polar coordinates are (2, 14 +360n) , (-2, 14+90+360n)

Answer 43

Yes that sounds good

Answer 44

ok thanks again. for all the help

Answer 45

The polar representation should be \[(r, \theta) = (r, \theta+2 \pi n)~~~\text{and}~~~(-r, \theta+(2n+1) \pi)\] I think I made a mistake, but your answers are right in any case

Answer 46

oh ok. :)

Answer 47

wait wait that should be an OR not an AND haha ok

Answer 48

lol its alright

Answer 49

xD

Answer 50

Ok have fun and take care haha

Answer 51

you too. Thanks again

Answer 52

Np :)