Write another representation for the point (1/2, 285°) where r<0.

Question

Write another representation for the point (1/2, 285°) where r<0.

Answer 1

285 degrees = 180 + 105 degrees, quadrant IV. reference angle is 75 degrees

1/2 = r = hypotenuse, solve for the two sides of the right triangle to get (x,y) = (rcos(theta), rsin(theta) = (1/2cos285, 1/2sin285) = about (0.129, -0.483)

(1/2, 285) = (r, theta) = in rectangular coordinates = (x,y) = (0.129, -0.483)

Answer 2

(1/2, 285°) = (- 1/2, 285° - 180°) = (- 1/2, 105°)