## anonymous one year ago Precalculus question: Determine two pairs of polar coordinates for the point (2, -2) with 0° ≤ θ < 360°. WILL MEDAL

1. triciaal

|dw:1439090016277:dw|

2. triciaal

hope something helped

3. triciaal

@jim_thompson5910 @UsukiDoll what am I missing?

4. UsukiDoll

I've seen similar questions like these online (2,-2) means that we are at the fourth quadrant and only cosine is positive. (x,y) ->(2,-2) is the rectangular coordinate so we need to switch to polar coordinates $x^2+y^2=r^2$ $(2)^2+(-2)^2=r^2$ $4+4=r^2$ $8=r^2$ $2 \sqrt{2}, -2 \sqrt{2}=r$ the value of tangent is indeed negative in the second and fourth quadrants.

5. UsukiDoll

OH GAWD y'all scared me *faints*

6. UsukiDoll

anyway $\tan(\theta) = -1$ is negative 45 degrees. so counter clockwise.

7. triciaal

@UsukiDoll thanks I have all that what am I missing (except r = -2sqrt2)

8. UsukiDoll

polar coordinates $(r, \theta)$ since $r = 2 \sqrt{2} , -2 \sqrt{2}$ $(2 \sqrt{2} , \theta)$, $(-2 \sqrt{2}, \theta)$ now to find theta....

9. UsukiDoll

hmmmmm... if we have negative 45 degrees... maybe 360 - 45 = 315 degrees for the fourth quadrant and 180-45 = 135 degrees for the second quadrant. I might be a bit off on this one since it has been a while.

10. UsukiDoll

oh wait... maybe.. |dw:1439093531632:dw|

11. UsukiDoll

|dw:1439093615408:dw| a bit sketchy on this part though.

12. UsukiDoll

uh oh... I missed something no wonder XD $x=rcos(\theta)$ if $r = 2\sqrt{2}$ $2=2\sqrt{2}cos(\theta)$ $\frac{1}{\sqrt{2}}=cos(\theta)$ that's 45 degrees $y=rsin(\theta)$ if $r = 2\sqrt{2}$ $-2=2\sqrt{2}sin(\theta)$ $-\frac{1}{\sqrt{2}}=sin(\theta)$ that's negative 45 degrees

13. UsukiDoll

If $r = -2\sqrt{2}$ and (2,-2) $x = r \cos(\theta)$ $2 = -2\sqrt{2} \cos(\theta)$ $-\frac{1}{\sqrt{2}} = \cos(\theta)$ that's negative 45 degrees $-2 = -2\sqrt{2} \sin(\theta)$ $\frac{1}{\sqrt{2}} = \sin(\theta)$ that's 45 degrees

14. triciaal

@UsukiDoll thanks for coming and agreeing @Jim_thompson5910 thanks for coming @jdoherty solution 2rt2, 135 2rt2, 315 the angle was -45 degrees