Question

Convert the point (x,y)=(−23 ,−2) into polar coordinates (r,θ) with r∈[0,[infinity]) and θ∈[0,2π).

Answer 1

To convert the point (-23, -2) into polar coordinates (r, θ), use the equations r = sqrt(x^2 + y^2) and θ = atan2(y, x). Apply these equations to obtain the polar coordinates.

Step-by-step explanation:

To convert the point (x, y) = (-23, -2) into polar coordinates (r, θ), we can use the equations r = sqrt(x^2 + y^2) and θ = atan2(y, x). Applying these equations, we get:

r = sqrt((-23)^2 + (-2)^2) = sqrt(529 + 4) = sqrt(533)

θ = atan2((-2), (-23)) = atan2(-2, -23)

Therefore, the polar coordinates for the point (-23, -2) are approximately (r, θ) = (sqrt(533), atan2(-2, -23)).