How do you convert (-3,3)(−3,3) to polar form?

1 Answer
P dilip_k
Mar 5, 2016

(3sqrt2,3pi/4)(3√2,3π4)

Explanation:

If Cartesian coordinate of point is (x,y)
and its polar coordinate is (r,theta) (r,θ)
then x=rcostheta x=rcosθand y=rsinthetay=rsinθ
given x= -3 then -3=rcostheta−3=rcosθ
and y= 3 ,So 3=rsintheta3=rsinθ
tantheta=-1tanθ=−1
both tantheta ,costhetatanθ,cosθ are negative and sin thetasinθ is poitive So the angletheta θ will be in 2nd quadrant
Hencetheta =pi-pi/4=3pi/4θ=π−π4=3π4
r^2= 3^2+(-3)^2r2=32+(−3)2
r=3sqrt2r=3√2
hence reqd polar coordinate is(3sqrt2,3pi/4)(3√2,3π4)

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