Answer:
the rectangular coordinates of the point (9, 150°) are approximately (-4.5, 7.794).
Explanation:
To convert from polar coordinates to rectangular coordinates, we use the following formulas:
x = r cos θ
y = r sin θ
where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point, measured counterclockwise.
In this case, r = 9 and θ = 150°. However, we need to convert θ to radians before we can use the formulas. We know that 180° = π radians, so:
150° = (5/6)π radians
Now we can use the formulas:
x = r cos θ = 9 cos (5/6)π ≈ -4.5
y = r sin θ = 9 sin (5/6)π ≈ 7.794
Therefore, the rectangular coordinates of the point (9, 150°) are approximately (-4.5, 7.794).