Determine the quadrant of a given angle in radians on the unit circle
Answer 1
Thomas Walker
To determine the quadrant of an angle $ \theta $ in radians on the unit circle, follow these steps:
1. If $ \theta $ is greater than $ 2\pi $ or less than $ -2\pi $, reduce it by subtracting or adding multiples of $ 2\pi $ until it is within the range $ [0, 2\pi] $.
2. Check the reduced angle:
– If $ 0 \leq \theta < \frac{\pi}{2} $, the angle is in Quadrant I.
– If $ \frac{\pi}{2} \leq \theta < \pi $, the angle is in Quadrant II.
– If $ \pi \leq \theta < \frac{3\pi}{2} $, the angle is in Quadrant III.
– If $ \frac{3\pi}{2} \leq \theta < 2\pi $, the angle is in Quadrant IV.
Answer 2
Amelia Mitchell
To determine the quadrant of an angle $ heta $ in radians on the unit circle, follow these steps:
1. Normalize $ heta $ to be within the range $ [0, 2pi] $ by adding or subtracting multiples of $ 2pi $.
2. Identify the quadrant:
– If $ 0 leq heta < frac{pi}{2} $, it is in Quadrant I.
– If $ frac{pi}{2} leq heta < pi $, it is in Quadrant II.
– If $ pi leq heta < frac{3pi}{2} $, it is in Quadrant III.
– If $ frac{3pi}{2} leq heta < 2pi $, it is in Quadrant IV.
Answer 3
Alex Thompson
To determine the quadrant of an angle $ heta $ in radians on the unit circle:
1. Normalize $ heta $ to $ [0, 2pi] $.
2. Check:
– $ 0 leq heta < frac{pi}{2} $: Quadrant I.
– $ frac{pi}{2} leq heta < pi $: Quadrant II.
– $ pi leq heta < frac{3pi}{2} $: Quadrant III.
– $ frac{3pi}{2} leq heta < 2pi $: Quadrant IV.
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