Answer:
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 - [tex]tan^{-1}(\frac{y}{x})[/tex] ] (neglect the negative sign of y-coordinate)
∵ x = 6 and y = -3
∵ r > 0
∵ [tex]r=\sqrt{x^{2}+y^{2}}[/tex]
- Substitute x and y in the rule of r
∴ [tex]r=\sqrt{(6)^{2}+(-3)^{2}}[/tex]
∴ [tex]r=\sqrt{36+9}[/tex]
∴ [tex]r=\sqrt{45}[/tex]
∴ [tex]r=3\sqrt{5}[/tex]
Now let us find Ф
∵ 0 ≤ Ф < 2π
∴ Ф = 2π - [tex]tan^{-1}(\frac{y}{x})[/tex]
- Neglect the negative sign of the y-coordinate
∴ Ф = 2π - [tex]tan^{-1}(\frac{3}{6})[/tex]
∴ Ф = 333.4° OR Ф = 5.82 radiant
∴ The polar coordinates is (3√5 , 333.4°) OR (3√5 , 5.82 rad)
