anonymous one year ago PLEASE Determine two pairs of polar coordinates for the point (5, -5) with 0° ≤ θ < 360°. (5 square root of 2, 315°), (-5 square root of 2, 135°) (5 square root of 2, 45°), (-5 square root of 2, 225°) (5 square root of 2, 135°), (-5 square root of 2, 315°) (5 square root of 2, 225°), (-5 square root of 2, 45°)

1. cwrw238

Hint the point is in the 4th quadrant

2. dumbcow

|dw:1440031939497:dw|

3. anonymous

I'm not sure what you mean. I have never worked with this kind of problem before..

4. dumbcow

|dw:1440032084293:dw|

5. dumbcow

ok when converting to polar form use following equations for given point (x,y) $r = \sqrt{x^2 + y^2}$ $\tan \theta = \frac{y}{x}$

6. anonymous

Okay so polar coordinates are the opposite coordinates?

7. anonymous

Okay

8. anonymous

so $r=\sqrt{5^2+(-5^2)}$

9. anonymous

therefore r= $\sqrt{50}$

10. dumbcow

now there are multiple ways of writing a given point in polar form different angles can be used as long as tan = y/x r can be neg, which reflects the point 180 degrees

11. dumbcow

correct, simplify the radical $\sqrt{50} = 5 \sqrt{2}$

12. anonymous

Alright, and I got $\tan \theta=-5/5$

13. anonymous

=-1

14. anonymous

theta = tan^-1(-1)

15. anonymous

so theta= -pi/4

16. anonymous

What am I to do with this information?

17. dumbcow

ok good so we have 1 angle (-45 or -pi/4) now use my circle drawings above to see how to get an equivalent angle

18. anonymous

I dont understand..I can see the equivalent angle

19. anonymous

I just dont know how to get it

20. dumbcow

here is a general form showing all 4 possible points for a given (x,y) $(r,\theta)$ $(r, \theta +2\pi)$ $(-r, \theta + \pi)$ $(-r, \theta - \pi)$

21. dumbcow

|dw:1440033135732:dw|

22. anonymous

So what would be my theta and my r?

23. dumbcow

you already calculated those ..... r = sqrt(50) , theta = pi/4

24. dumbcow

sorry -pi/4

25. anonymous

Oh, okay. I would have the following possible answers then: A. $5\sqrt{2},-\left(\begin{matrix}\pi \\ 4\end{matrix}\right)$ B. $5\sqrt{2},-\left(\begin{matrix}\pi \\ 4\end{matrix}\right)+2pi$ C. $-5\sqrt{2},-\left(\begin{matrix}\pi \\ 4\end{matrix}\right)+pi$ D. $-5\sqrt{2},-\left(\begin{matrix}\pi \\ 4\end{matrix}\right)-pi$

26. anonymous

what do you mean by 'find 2 match the given pairs'

27. dumbcow

figure it out...gotta go good luck!

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