$ ext{What is the cosine of the angle } frac{pi}{3} ext{ on the unit circle?}$
Answer 1
Sophia Williams
To find the cosine of the angle \( \frac{\pi}{3} \) on the unit circle, we need to locate this angle on the circle.
The angle \( \frac{\pi}{3} \) corresponds to 60 degrees.
On the unit circle, the coordinates of the point at angle \( \frac{\pi}{3} \) are \( \left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right) \).
The cosine of an angle is the x-coordinate of the corresponding point on the unit circle.
Therefore, \( \cos \left( \frac{\pi}{3} \right) = \frac{1}{2} \).
Answer 2
Emily Hall
Finding the cosine value of ( frac{pi}{3} ) involves identifying this angle on the unit circle.
The angle ( frac{pi}{3} ) is equivalent to 60 degrees.
On the unit circle, the point for angle ( frac{pi}{3} ) is ( left( frac{1}{2}, frac{sqrt{3}}{2}
ight) ).
The x-coordinate provides the cosine value.
Thus, ( cos left( frac{pi}{3}
ight) ) is ( frac{1}{2} ).
Answer 3
Maria Rodriguez
To find ( cos(frac{pi}{3}) ), use the unit circle.
The angle ( frac{pi}{3} ) corresponds to 60 degrees and has coordinates ( left( frac{1}{2}, frac{sqrt{3}}{2}
ight) ).
Therefore, ( cos(frac{pi}{3}) = frac{1}{2} ).
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