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

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

Mathematics
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hey i actually got stuck @Astrophysics
Hey, no worries, where did you get stuck?

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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
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
r = 5sqrt(2)
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?
yea i got that
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
ok so tan(theta) = -5/5
???
Yes exactly!
tan(theta) = -1 from here to I inverse it?
Yup \[\theta = \tan^{-1}(-1)\]
ok give me a sec
7pi/4
Good so that is 315 degrees
ok so it would be 5sqrt(2),315
Yes, and the other you want for \[-5\sqrt{2}\]
Which is just 315-180
135
Bingo
so the answer is A?
Sounds good!
Thank you so much for the help! :)
Np :)
x is positive and y is negative so it is below x-axis x is positive , yis negative ,hence in fourth quadrant.
Yup I already had shown that in the previous post ;P
you mind helping me with one more? sorry. lol
Sure haha
Find all polar coordinates of point P = (2, 14°)
n is an integer
x = 1.94059 y = 0.48384
Ok maybe I shouldn't have wrote that just ignore it and look at what I said after
lol ok
so would it just be (2, 14 +/- 2npi) ???
Yes that works (2, 14 +360n) as we're using degrees
is that it?
yes or (-2, 14+90+360n)
wait im confused now where did the 90 come from?
Look at what I said twice, the polar representations
so all the polar coordinates are (2, 14 +360n) , (-2, 14+90+360n)
Yes that sounds good
ok thanks again. for all the help
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
oh ok. :)
wait wait that should be an OR not an AND haha ok
lol its alright
xD
Ok have fun and take care haha
you too. Thanks again
Np :)

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