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

Question

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

anonymous · Answer

I know that it is (5sqrt2, an angle) then (-5sqrt2, an angle)

terenzreignz · Answer

Well, that angle would have for its tangent, y/x
Your y is -5
and x is 5

What's y/x?

anonymous · Answer

-1

terenzreignz · Answer

Good :)
Now which angle(s) has a tangent of -1?

anonymous · Answer

That IDK

terenzreignz · Answer

Then, you can either use a scientific calculator (if permitted) or consult your unit circle again.

anonymous · Answer

I can use a scientific calc, but what would i do ?

terenzreignz · Answer

input $\large \tan^{-1}(-1)$

anonymous · Answer

ohhh arctan!

terenzreignz · Answer

yes, arctan.

anonymous · Answer

okay one sec

anonymous · Answer

its -45

anonymous · Answer

The two angles are different right? so if one of them is -45 then what is the other?

terenzreignz · Answer

-45?
That's not within your bounds...
0° ≤ θ < 360°

anonymous · Answer

okay then the flip of -45 is 315

terenzreignz · Answer

Good :)
And there's another angle for which tangent is -1.
Unfortunately, your calculator can't help you with that :)

terenzreignz · Answer

Unless....

terenzreignz · Answer

never mind that other angle. Just know that there should be two possible angles.
but we have more info...
Your point (5,-5), in which quadrant is it?

anonymous · Answer

IV right

terenzreignz · Answer

Right. And 315 degrees, in which quadrant is that?

anonymous · Answer

II   I
III  IV
so its in 4 ?

terenzreignz · Answer

Yes :)
So, it seems you lucked out and picked the correct quadrant :)

anonymous · Answer

idk how to tell the quadrants of angles though

terenzreignz · Answer

oh...
0-90 is 1
90-180 is 2
180-270 is 3
270-360 is 4

anonymous · Answer

ohhh okay cool so then i was right :P

anonymous · Answer

so it is in the fourth quadrant... what does thatmean for me?

terenzreignz · Answer

It means you picked the correct angle.
As I said before, there are two possible angles for which the tangent is -1
One is 315 degrees
the other is 135 degrees.
But 135 degrees is in quadrant II

and your point (5, -5) is in quadrant IV
so it has to be 315 degrees.

Savvy? :D

anonymous · Answer

ohhhhhhhhhhh! so i see! but then doesnt that make 135 the other angle?

terenzreignz · Answer

It does :)
Your intuition is brilliant :)
The 'rejected' angle would be the angle for the coordinates with the 'negative' r :)

anonymous · Answer

Got it! Thanks man! just one more on this wretched topic then ill be done. Can I tag you again?

terenzreignz · Answer

Sure :)