How do you convert (-6,-3) into polar coordinates?

1 Answer
Shwetank Mauria
Feb 13, 2016

Polar coordinates of (−6,−3) are (3sqrt5, 206.565^o)

Explanation:

If (x, y) are converted into polar coordinates (r, theta),

while (x, y) in terms of r and theta are x=rcostheta and y=rsintheta, (r, theta) in terms of x and y are r=sqrt(x^2+y^2) and theta=tan^-1(y/x)

Hence, converting (−6,−3) into polar coordinates

r=sqrt((-6)^2+(-3^2) = sqrt45 = 3sqrt5

theta=tan^-1((-3)/-6) = tan^-1(1/2). Further, as (−6,−3) is in third quadrant theta=(180+26.565)=206.565^o

Hence polar coordinates of (−6,−3) are (3sqrt5, 206.565^o)

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