## anonymous one year ago Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.

1. anonymous

so right now I have $\cos(\theta) = \frac{ 4 }{ 4\sqrt{2} }$ and $\sin(\theta)=-\frac{ 4 }{ 4\sqrt{2} }$ but i dont know where to go from here... please help!

2. jim_thompson5910

the 4's cancel leaving with 1 over sqrt(2) for the first fraction

3. jim_thompson5910

$\Large \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$

4. anonymous

alright, but how do i make that a polar coordinate. i need to take the arc sin according to the examples in my book but that doesnt work here

5. anonymous

and the arc cos

6. jim_thompson5910

you can use the unit circle

7. anonymous

oh wait cause now they are known values on the unit circle

8. jim_thompson5910

look on the unit circle where the x coordinate is $$\Large \frac{1}{\sqrt{2}}$$ or $$\Large \frac{\sqrt{2}}{2}$$

9. anonymous

315

10. anonymous

ok so the first polar coordinate would be $\left( 4\sqrt{2} , 315\right)$

11. jim_thompson5910

yes

12. anonymous

how would i find a second one equal to that?

13. jim_thompson5910

|dw:1439180139138:dw|

14. jim_thompson5910

|dw:1439180155156:dw|

15. jim_thompson5910

Draw a line from (4,-4) through the origin |dw:1439180192858:dw|

16. jim_thompson5910

|dw:1439180205002:dw|

17. anonymous

so that would be 135 degrees?

18. jim_thompson5910

yes so another polar point would be $$\Large \left( -4\sqrt{2} , 135\right)$$

19. anonymous

ah ok, thank you for your help!

20. jim_thompson5910

you start at the origin facing directly east then you turn 135 degrees counter clockwise still facing this direction, you walk backwards (hence the negative r value) 4*sqrt(2) units

21. anonymous

alright that makes sense

22. anonymous

thank you!

23. jim_thompson5910

no problem

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