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A point is at an angle of 250° on the unit circle…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A point is at an angle of on the unit circle. In which quadrant is it? The reference angle is how far the point is from the nearest part of the x-axis. Find the reference angle, and the cosine of .
Need a reminder? The key ideaShow
Degrees to radians: multiply by . Python's trigonometric functions take radians: math.sin(math.radians(d)). The point at angle on the unit circle is . Floats carry a rounding error of about , so compare them with math.isclose, not ==.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Quadrant. , so the point is in quadrant III.
Step 2. Reference angle. .
Step 3. Cosine. In quadrant III the cosine is negative, and its size is that of the reference angle: .
Answer: quadrant III, a reference angle of , and .
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