Determine two pairs of polar coordinates for the point (5, -5) with 0° ≤ θ < 360°.

Accepted Solution

Answer:(5,-5) can be represented in polar form by [tex](2\sqrt{5},315^\circ)[/tex] and [tex](-2\sqrt{5},135^\circ)[/tex]Step-by-step explanation:polar coordinates use a distance and an angleit would be like (x,y) but x is distance from origin to point and y is the angle measured counterclockwise from the positive x-axis.for (5,-5)first find the distance to that point using distance formuladistance from (0,0) to (5,-5) is[tex]D=\sqrt{(0-5)^2+(0-(-5))^2}[/tex][tex]D=\sqrt{25+25}[/tex][tex]D=5\sqrt{2}[/tex]so our point has to be in the form [tex](x,y)[/tex] where [tex]\mid x\mid=5\sqrt{2}[/tex]now finding the degreeusing inverse tangent[tex]tan^{-1}(\frac{-5}{5})=-45^\circ[/tex]if we look on the graph, it is also 360-45=315 degrees from positive x axisso one polar coordiante is [tex](2\sqrt{5},315^\circ)[/tex]the other one is in the oposite sidewe add or subtract 180 degrees and make the sign of x negative to go in the oposite directionsubtraction 180 to get 135 degreesso the other point is [tex](-2\sqrt{5},135^\circ)[/tex](5,-5) can be represented in polar form by [tex](2\sqrt{5},315^\circ)[/tex] and [tex](-2\sqrt{5},135^\circ)[/tex]