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How do you change the polar coordinate #(9, -pi/3)# into rectangular coordinates?

Answer 1

James Adkins

#(4.5,-7.79)#

To convert from polar coordinate to rectangular coordinate we use the formula #x=rcos theta, y=rsin theta#

Hence,

#x=9cos (-(pi)/3)=4.5#

#y=9 sin (-(pi)/3)~~-7.79#

So the point is approximately #(4.5,-7.79)#

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Answer 2

Emery Adkins

To change the polar coordinate (9, -π/3) into rectangular coordinates, you can use the following formulas:

[ x = r \cdot \cos(\theta) ] [ y = r \cdot \sin(\theta) ]

Substitute ( r = 9 ) and ( \theta = -\frac{\pi}{3} ) into these formulas:

[ x = 9 \cdot \cos\left(-\frac{\pi}{3}\right) ] [ y = 9 \cdot \sin\left(-\frac{\pi}{3}\right) ]

Calculate the values:

[ x = 9 \cdot \frac{1}{2} = 4.5 ] [ y = 9 \cdot \left(-\frac{\sqrt{3}}{2}\right) = -\frac{9\sqrt{3}}{2} ]

So, the rectangular coordinates are (4.5, -4.5√3).

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Answer from HIX Tutor

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