Determine the Quadrant of a Given Point on a Unit Circle
Answer 1
Charlotte Davis
Given the point \((x, y)\) on a unit circle, determine the quadrant in which the point lies.
The unit circle has a radius of 1. The quadrants are defined as follows:
– Quadrant I: \((x > 0, y > 0)\)
– Quadrant II: \((x < 0, y > 0)\)
– Quadrant III: \((x < 0, y < 0)\)
– Quadrant IV: \((x > 0, y < 0)\)
Let’s solve for the point \((-\frac{1}{2}, \frac{\sqrt{3}}{2})\)
Given: \(x = -\frac{1}{2}\) and \(y = \frac{\sqrt{3}}{2}\)
Since \(x < 0\) and \(y > 0\), the point lies in Quadrant II.
Answer 2
Ava Martin
Consider the point ((frac{sqrt{2}}{2}, -frac{sqrt{2}}{2})) on the unit circle. Determine the quadrant.
The unit circle has a radius of 1. The quadrants are defined as follows:
– Quadrant I: ((x > 0, y > 0))
– Quadrant II: ((x < 0, y > 0))
– Quadrant III: ((x < 0, y < 0))
– Quadrant IV: ((x > 0, y < 0))
Given: (x = frac{sqrt{2}}{2}) and (y = -frac{sqrt{2}}{2})
Since (x > 0) and (y < 0), the point lies in Quadrant IV.
Answer 3
Henry Green
Determine the quadrant for the point ((0.5, -0.5)) on the unit circle.
The unit circle has a radius of 1. The quadrants are defined as follows:
– Quadrant I: ((x > 0, y > 0))
– Quadrant II: ((x < 0, y > 0))
– Quadrant III: ((x < 0, y < 0))
– Quadrant IV: ((x > 0, y < 0))
Given: (x = 0.5) and (y = -0.5)
Since (x > 0) and (y < 0), the point lies in Quadrant IV.
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