Get the answer to "The rectangular coordinates of a point are (-4,..."

College
Calculus and Analysis
Integral Calculus
Parametric equations, polar coordinates, and vector-valued functions

Bevan Mcdonald

Answered question

2021-02-09

The rectangular coordinates of a point are (-4, 4). Find polar coordinates of the point.

Answer & Explanation

au4gsf

Skilled2021-02-10Added 95 answers

We have been given the rectangular coordinates (-4,4) and we have to find the polar coordinates of the points. as we know that $r = \sqrt{(} x^{2} + y^{2})$ now as rectangular coordinates are (x, y) and polar coordinates are $(r, θ)$ . $r = \sqrt{(- 4)^{2} + 4^{2}}$
$r = \sqrt{16 + 16}$
$r = \sqrt{32}$
$r = 4 \sqrt{2}$ now as we know that $α = t a n^{-} 1 \frac{y}{x}$ $a = t a n^{-} 1 \frac{4}{- 4}$
$a = t a n^{-} 1 (- 1)$
$a = - \frac{π}{4}$
$θ = - π / 4 + π = \frac{3 π}{4}$
$θ = \frac{3 π}{4}$ now The required polar coordinate $= (4 \sqrt{2}, 3 \frac{π}{4})$

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