Answer:
C
Step-by-step explanation:
To convert from polar to rectangular form, that is
(r, Θ ) → (x, y ), use the conversion
x = r cosΘ and y = r sinΘ
Here r = 4 and Θ = [tex]\frac{3\pi }{2}[/tex], thus
x = 4 × cos([tex]\frac{3\pi }{2}[/tex]) = 4 × 0 = 0
y = 4 × sin( [tex]\frac{3\pi }{2}[/tex]) = 4 × - 1 = - 4
Thus rectangular form = (0, - 4 ) → C
OPTION C IS CORRECT.
The coordinates in the rectangular system are (0, -4).
We have the coordinates of a point 'P' in polar form as P(4, [tex]\frac{3\pi }{2}[/tex]).
We have to convert it into the rectangular coordinates.
The relation between the coordinates in polar form and rectangular form is as follows -
x = r cosθ
y = r sinθ
We can use the above equations in order to find the coordinates in the rectangular cartesian system. In the question given -
r = 4 and θ = [tex]\frac{3\pi }{2}[/tex]
Substituting the values, we get -
x = 4 cos ( [tex]\frac{3\pi }{2}[/tex]) = 4 x 0 = 0
y = 4 sin ([tex]\frac{3\pi }{2}[/tex]) = 4 x -1 = -4
Hence, the coordinates in the rectangular system are (0, -4).
To solve more questions on converting from polar coordinates to rectangular coordinates, visit the link below -
https://brainly.com/question/13103661
#SPJ2
