Answer:
2nd option
Step-by-step explanation:
To convert from (x, y ) → (r, θ )
where
r = [tex]\sqrt{x^2+y^2}[/tex]
θ = [tex]tan^{-1}[/tex] ([tex]\frac{y}{x}[/tex] )
Here (x, y ) = (- 4, 5 ), a point in the 2nd quadrant
r = [tex]\sqrt{(-4)^2+5^2}[/tex] = [tex]\sqrt{16+25}[/tex] = [tex]\sqrt{41}[/tex]
θ = [tex]tan^{-1}[/tex] ([tex]\frac{5}{4}[/tex] ) ≈ 51.3° ← related acute angle , then
θ = 180° - 51.3° = 128.7°
Thus
(- 4, 5 ) → ([tex]\sqrt{41}[/tex], 128.7° ) in polar form