"What is (-2, 9) in polar coordinates?" was answered by students like you

High School
Calculus and Analysis
Calculus 2
Parametric equations

Cooper Weber

Answered question

2022-02-04

What is (-2, 9) in polar coordinates?

Answer & Explanation

Ijezid8t

Beginner2022-02-05Added 13 answers

Step 1
The polar coordinates $(r, θ)$ of a point in the plane are related to the rectangular coordinates of the point by the equations
$r^{2} = x^{2} + y^{2}$ and $\tan (θ) = \frac{y}{x}$ (when $x \neq 0$ )
Since the point whose rectangular coordinates are $(x, y) = (- 2, 9)$ is in the 2nd quadrant of the plane, if we take $r = \sqrt{x^{2} + y^{2}} = \sqrt{4 + 81} = \sqrt{85}$ , then we need to add $π$ rediants to the output of the arctangent function to find the angle:
$θ = \arctan (\frac{y}{x}) + π = \arctan (\frac{9}{- 2}) + π = \arctan (- \frac{9}{2}) + π$

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