Determine the quadrant of a point on the unit circle given by an angle $ heta $
Answer 1
Thomas Walker
Given an angle $ \theta $, we need to determine in which quadrant the corresponding point on the unit circle lies. The quadrants are determined as follows:
1. If $ 0 \leq \theta < \frac{\pi}{2} $, the point is in the first quadrant.
2. If $ \frac{\pi}{2} \leq \theta < \pi $, the point is in the second quadrant.
3. If $ \pi \leq \theta < \frac{3\pi}{2} $, the point is in the third quadrant.
4. If $ \frac{3\pi}{2} \leq \theta < 2\pi $, the point is in the fourth quadrant.
Answer 2
Alex Thompson
Given an angle $ heta $, we determine its quadrant on the unit circle:
1. For $ 0 leq heta < frac{pi}{2} $, the point lies in the first quadrant.
2. For $ frac{pi}{2} leq heta < pi $, the point lies in the second quadrant.
3. For $ pi leq heta < frac{3pi}{2} $, the point lies in the third quadrant.
4. For $ frac{3pi}{2} leq heta < 2pi $, the point lies in the fourth quadrant.
Answer 3
William King
For a given angle $ heta $:
1. $ 0 leq heta < frac{pi}{2} $: first quadrant.
2. $ frac{pi}{2} leq heta < pi $: second quadrant.
3. $ pi leq heta < frac{3pi}{2} $: third quadrant.
4. $ frac{3pi}{2} leq heta < 2pi $: fourth quadrant.
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