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

Answer 1

#(3sqrt2,3pi/4)#

If Cartesian coordinate of point is (x,y) and its polar coordinate is # (r,theta) # then #x=rcostheta #and #y=rsintheta# given x= -3 then #-3=rcostheta# and y= 3 ,So #3=rsintheta# #tantheta=-1# both #tantheta ,costheta# are negative and# sin theta# is poitive So the angle#theta # will be in 2nd quadrant Hence#theta =pi-pi/4=3pi/4# #r^2= 3^2+(-3)^2# #r=3sqrt2# hence reqd polar coordinate is#(3sqrt2,3pi/4)#

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Answer 2

Asher Friedman

To convert the point ((-3, 3)) from rectangular coordinates to polar form, we use the following formulas:

[ r = \sqrt{x^2 + y^2} ] [ \theta = \arctan\left(\frac{y}{x}\right) ]

Substitute the given coordinates ((-3, 3)) into these formulas:

[ r = \sqrt{(-3)^2 + (3)^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2} ] [ \theta = \arctan\left(\frac{3}{-3}\right) = \arctan(-1) = -\frac{\pi}{4} ]

So, the polar form of the point ((-3, 3)) is (3\sqrt{2} \text{ at } -\frac{\pi}{4}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.