- Translate each set of polar coordinates into rectangular coordinates.

- (4,π)

Answer

- To translate into rectangular coordinates we apply the formulas x = rcosθ and y = rsinθ.

- The point is in the second quadrant.

The rectangular coordinates are

which do indeed describe a point in the second quadrant.

- The point lies in the third quadrant.

The rectangular coordinates are

which do describe a point in the third quadrant.

- The point is in the third quadrant.

The rectangular coordinates are

which are indeed in the third quadrant.

- The point (4,π) is on the negative
*x*-axis.

- We don't need to bother with formulas because we can see immediately that the rectangular coordinates of this point are(x,y) = (-4,0).