Question

Choose the point which shows the correct location for the polar coordinate (-3,315°)

Answer 1

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

`\begin{gathered} x=-3.cos((7)/(4)\pi) \\ x=-3\cdot\frac{\sqrt[]{2}}{2} \end{gathered}`

Since 315º is on the Quadrant IV the sign for that is positive. Now let's find out the y-coordinate:

`\begin{gathered} y=-3\cdot\sin ((7)/(4)\pi) \\ y=-3\cdot(-\frac{\sqrt[]{2}}{2}) \\ y=\frac{3\sqrt[]{2}}{2} \end{gathered}`

3) Hence, the correct location for that Polar coordinate is found on D