What is another representation of the polar coordinate (8-45)?

Answer 1

53

Answer 2

The polar coordinates (8, -45°) refer to the angle as being 45° when measured in a clockwise direction from the origin on the x-axis.

Normally, polar coordinates measure the angle in an anticlockwise direction and an alternative form is thus (8, 315°).

The Cartesian coordinates of this point are (4√2, -4√2) or (5.657, -5,657) 3dp.

Answer 3

The Cartesian coordinates equivalent to the polar coordinates (r, theta) are (r*cos(theta), r*sin(theta)). In this example, r = 8 and theta = -45.

Assuming that theta is given in degrees, the equivalent Cartesian coordinates are [-4*sqrt(2), 4*sqrt(2)] or (-5.6569, 5.6569), approx.