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How do you find the polar coordinates of the point with rectangular coordinates #(-2,2# )?

Answer 1

William Abdalla

The rectangular coordinates #(x,y)=(-2,2)# are #(r,theta)=(2sqrt{2},{3pi}/4)# in polar coordinates.

Since #r# is the distance of the point from the origin,

#r-sqrt{x^2+y^2}=sqrt{(-2)^2+2^2}=sqrt{8}=2sqrt{2}#

Since the positive x-axis and the segment connecting the origin and the point make #135^circ={3pi}/4# rad,

#theta={3pi}/4#

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Answer 2

Elijah Abram

To find the polar coordinates of a point given its rectangular coordinates ((-2, 2)), you can use the formulas:

(r = \sqrt{x^2 + y^2})

(θ = \arctan{\left(\frac{y}{x}\right)})

Substitute (x = -2) and (y = 2) into these formulas:

(r = \sqrt{(-2)^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2})

(θ = \arctan{\left(\frac{2}{-2}\right)} = \arctan{(-1)})

Since (y) is positive and (x) is negative, (θ = \arctan{(-1)} = -\frac{\pi}{4}) (in radians) or (θ = 135^\circ) (in degrees).

Therefore, the polar coordinates of the point ((-2, 2)) are ((2\sqrt{2}, -\frac{\pi}{4})) in radians or ((2\sqrt{2}, 135^\circ)) in degrees.

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