Convert (-5,2) to polar coordinates?

r² = 25 + 4

r² = 29

r = √29

tan ∅ = - 2/5

∅ = 180° - 21•8 °

∅ = 158•2°

Point √29 /_158•2°

(-5,2)

r = √(x^2 + y^2)

r = √[(-5)^2 + 2^2]

r = 5.385

solving for the angle..

θ = tan^(-1) = y/x = 2/(-5) = 158.19°

r^2 = 25+4

r = √29

θ = arctan(-2/5) = 158.2°

(√29,158.2°)

Rule

point (a,b)

to polar [r, θ] , with

r = √ (a^2+b^2)

θ = cos^-1 (a/r) , if a<0

If cartesian coordinate is (x,y) then polar is (r,θ), where

r = √(x²+y²) and θ=tan⁻¹(y/x)

For (-5,2) polar coordinate is (√29,158.2°)

r = √((-5)²+2²) and θ=tan⁻¹(2/-5)

r = √29 and θ = 158.2° ( in 2nd quadrant)

r = √((-5)² + 2²) = √29 so

(-5,2) = ( √29, atan2(2, -5) ) polar ≈ (5.385, 158.2°) polar