Question

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

Answer 1

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!

Answer 2

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

Answer 3

\[\Large \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}\]

Answer 4

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

Answer 5

and the arc cos

Answer 6

you can use the unit circle

Answer 7

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

Answer 8

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

Answer 9

315

Answer 10

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

Answer 11

yes

Answer 12

how would i find a second one equal to that?

Answer 13

Draw a line from (4,-4) through the origin