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Given the polar coordinates (4,-pi/3) which of the following rectangular coordinate pairs represents the same point?

a) (-2,2sqrt3)
b) (2,-2sqrt3)
c) (2sqrt3,-2)
d) (2sqrt3, 2)

Sagot :

Facundo3141592idn

The rectangular point that represents (4, - pi/3) is the one in option b: (2, -2√3).

How to change the coordinates?

For a point (x, y), the polar coordinates are:

  • R = √(x^2 + y^2)
  • θ = atan(y/x).

Then we must have:

R = 4 =  √(x^2 + y^2)

Notice that for all the given points we have the radius equal to 4, so the only part that we care is the angle one:

-pi/3 = Atan(y/x)

tan(-pi/3) = y/x = -1.73

So, y and x must have different signs, and because the angle is negative, we will say that the y-component must be negative.

So the correct option will be b: (2, -2√3)

y/x = -2*√3/2 = √3 = -1.73

If you want to learn more about polar coordinates, you can read:

https://brainly.com/question/14965899

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