Convert the Cartesian coordinate (6,-3) to polar coordinates, 0≤θ<2π, r>0

The polar coordinates is (3√5 , 333.4°) OR (3√5 , 5.82 rad)

Step-by-step explanation:

The polar form of the Cartesian coordinates (x , y) is (r , Ф), where

The Cartesian coordinates is (6 , -3)

That means the point lies in the fourth quadrant because the x-coordinate is positive and the y-coordinate is negative, so Ф will be equal [2π -   ] (neglect the negative sign of y-coordinate)

∵ x = 6 and y = -3

∵ r > 0

∵

- Substitute x and y in the rule of r

∴

∴

∴

∴

Now let us find Ф

∵ 0 ≤ Ф < 2π

∴ Ф = 2π -  

- Neglect the negative sign of the y-coordinate

∴ Ф = 2π -  

∴ Ф = 333.4°  OR  Ф = 5.82 radiant

∴ The polar coordinates is (3√5 , 333.4°) OR (3√5 , 5.82 rad)

step-by-step explanation:

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