Find all polar representation of Cartesian point (-1,1)?

Answer 1

r = √1² + (-1)² = √2
θ = arctan(1/-1) = -π/4 ± n2π, where n is any integer.

Answer 2

The polar representation of (x, y) is (r, θ)
where
r = √(x² + y²) (x ≥ 0)
= -√(x² + y²) (x < 0)

and θ = arctan (y/x)

So for (-1, 1)
r = -√2
θ = -π/4

ie (-1, 1) ≡ (-√2, -π/4)

Answer 3

...x-----l 1
_l____l___
-1..... o

The angle is 45 + 90. The radius is sqrt 2, you calculate it using the Pythagoras Theorem

Ana