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

- anonymous

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

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- schrodinger

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- anonymous

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

- anonymous

hey i actually got stuck @Astrophysics

- Astrophysics

Hey, no worries, where did you get stuck?

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## More answers

- Astrophysics

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

- anonymous

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

- anonymous

r = 5sqrt(2)

- Astrophysics

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?

- anonymous

yea i got that

- Astrophysics

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

- anonymous

ok so tan(theta) = -5/5

- anonymous

???

- Astrophysics

Yes exactly!

- anonymous

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

- Astrophysics

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

- anonymous

ok give me a sec

- anonymous

7pi/4

- Astrophysics

Good so that is 315 degrees

- anonymous

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

- Astrophysics

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

- Astrophysics

Which is just 315-180

- anonymous

135

- Astrophysics

Bingo

- anonymous

so the answer is A?

- Astrophysics

Sounds good!

- anonymous

Thank you so much for the help! :)

- Astrophysics

Np :)

- anonymous

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

- Astrophysics

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

- anonymous

you mind helping me with one more? sorry. lol

- Astrophysics

Sure haha

- anonymous

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

- Astrophysics

n is an integer

- anonymous

x = 1.94059
y = 0.48384

- Astrophysics

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

- anonymous

lol ok

- anonymous

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

- Astrophysics

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

- anonymous

is that it?

- Astrophysics

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

- anonymous

wait im confused now where did the 90 come from?

- Astrophysics

Look at what I said twice, the polar representations

- anonymous

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

- Astrophysics

Yes that sounds good

- anonymous

ok thanks again. for all the help

- Astrophysics

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

- anonymous

oh ok. :)

- Astrophysics

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

- anonymous

lol its alright

- Astrophysics

xD

- Astrophysics

Ok have fun and take care haha

- anonymous

you too. Thanks again

- Astrophysics

Np :)

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