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daser333 [38]
3 years ago
6

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

Mathematics
1 answer:
MatroZZZ [7]3 years ago
6 0

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

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