Precalculus: polar to rectangle coordinated

Question

1. (-6, -pi/4)
2. (-2, 3pi/4)

Answer 1

This direction is much easier.

From (r, Θ), you get (x, y) with these equations:

x = r cos Θ

y = r sin Θ

(-6, -π/4)

x = -6 cos -π/4 = -6 • √2/2 = -3√2

y = -6 sin -π/4 = -6 • -√2/2 = 3√2

Answer : (-3√2 , 3√2)

(-2 3π/4)

x = -2 cos 3π/4 = -2 • -√2/2 = √2

y = -2 sin 3π/4 = -2 • √2/2 = -√2

Answer : (√2 , -√2)