D
1) Since the point we want to locate is (-3, 315º) Then we need to apply the following formulas:
x= r.cos (θ)
y = r * sin (θ)
2) Now, we'll plug into that the given coordinates. Converting 315º to radians:
2π ------360
x -------- 315
x= 315*2π/360
x=7/4π
[tex]\begin{gathered} x=-3.cos(\frac{7}{4}\pi) \\ x=-3\cdot\frac{\sqrt[]{2}}{2} \end{gathered}[/tex]
Since 315º is on the Quadrant IV the sign for that is positive. Now let's find out the y-coordinate:
[tex]\begin{gathered} y=-3\cdot\sin (\frac{7}{4}\pi) \\ y=-3\cdot(-\frac{\sqrt[]{2}}{2}) \\ y=\frac{3\sqrt[]{2}}{2} \end{gathered}[/tex]
3) Hence, the correct location for that Polar coordinate is found on D
