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On a circle of radius 2, center (0, 0), find the x and y coordinates at angle 270 degrees (or 3π/2 in radian measure).

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Solution

To find the x and y coordinates on a circle at a given angle, we can use the equations:

x = rcos(θ) y = rsin(θ)

where r is the radius of the circle, θ is the angle in radians, and (x, y) are the coordinates on the circle.

Given that the radius r = 2 and the angle θ = 270 degrees = 3π/2 radians, we can substitute these values into the equations:

x = 2cos(3π/2) = 20 = 0 y = 2sin(3π/2) = 2(-1) = -2

So, the coordinates at angle 270 degrees (or 3π/2 in radian measure) on the circle of radius 2, center (0, 0), are (0, -2).

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