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

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Answer 1 · 2016-05-28T02:12:39

$(r, theta)=(3sqrt 2, (7pi)/4)$ or $(3sqrt 2, -pi/4)$

Use $(x, y) = (3, -3)= (r cos theta, r sin theta)$

$r=sqrt(x^2+y^2)=sqrt(9+9)=3 sqrt 2$

$cos theta = 1/sqrt 2>0 and sin theta -1/sqrt2<0$

So, theta is in the 4th quadrant and is $(7pi)/4$ and this direction is

same as for $-pi/4$ .

Now, $(r, theta)=(3sqrt 2, (7pi)/4))$ or $(3sqrt 2, -pi/4)$ .

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