Question

Which polar coordinates represent the same point as the rectangular coordinates (-4,5)?

Answer 1

Answer:

2nd option

Step-by-step explanation:

To convert from (x, y ) → (r, θ )

where

r = $\sqrt{x^2+y^2}$

θ = $tan^{-1}$ ($\frac{y}{x}$ )

Here (x, y ) = (- 4, 5 ), a point in the 2nd quadrant

r = $\sqrt{(-4)^2+5^2}$ = $\sqrt{16+25}$ = $\sqrt{41}$

θ = $tan^{-1}$ ($\frac{5}{4}$ ) ≈ 51.3° ← related acute angle , then

θ = 180° - 51.3° = 128.7°

Thus

(- 4, 5 ) → ($\sqrt{41}$, 128.7° ) in polar form