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

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

Mathematics
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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!
the 4's cancel leaving with 1 over sqrt(2) for the first fraction
\[\Large \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}\]

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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
and the arc cos
you can use the unit circle
oh wait cause now they are known values on the unit circle
look on the unit circle where the x coordinate is \(\Large \frac{1}{\sqrt{2}}\) or \(\Large \frac{\sqrt{2}}{2}\)
315
ok so the first polar coordinate would be \[\left( 4\sqrt{2} , 315\right)\]
yes
how would i find a second one equal to that?
|dw:1439180139138:dw|
|dw:1439180155156:dw|
Draw a line from (4,-4) through the origin |dw:1439180192858:dw|
|dw:1439180205002:dw|
so that would be 135 degrees?
yes so another polar point would be \(\Large \left( -4\sqrt{2} , 135\right)\)
ah ok, thank you for your help!
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
alright that makes sense
thank you!
no problem

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