The rectangular coordinates of a point are given (2, -2). Find polar coordinates of the point. Express theta in radians.

Ernstfalld 2020-12-22 Answered
The rectangular coordinates of a point are given (2, -2). Find polar coordinates of the point. Express theta in radians.
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Expert Answer

yunitsiL
Answered 2020-12-23 Author has 108 answers

Let the given rectangular coordinates be (x, y). Then, (x,y)=(2,2) Let polar coordinates be =(r,θ) Then using formulas - r=x2+y2
θ=tan1(yx) Using equation (1) - r=x2+y2
r=(2)2+(2)2
r=4+4
r=8
r=22 Now θ=tan1(yx)
θ=tan1(22)
θ=tan1(1)
θ=tan1(1)[tan1(x)=tan1(x)]
θ=tan1(tanπ/4)
θ=π/4 Hence, Polar coordinates = (r,θ)=(22,π4)

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