$ ext{Find the value of cosine for an angle on the unit circle}$
Answer 1
Mia Harris
Let’s find the value of $\cos(\frac{\pi}{4})$ on the unit circle.
The angle $\frac{\pi}{4}$ is equivalent to 45 degrees.
On the unit circle, the coordinates of the point at an angle of $\frac{\pi}{4}$ are $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$.
Thus, the cosine of $\frac{\pi}{4}$ is $\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$.
Answer 2
Samuel Scott
Determine the value of $cos(frac{2pi}{3})$ on the unit circle.
The angle $frac{2pi}{3}$ is equivalent to 120 degrees.
On the unit circle, the coordinates of the point at an angle of $frac{2pi}{3}$ are $(-frac{1}{2}, frac{sqrt{3}}{2})$.
Therefore, the cosine of $frac{2pi}{3}$ is $cos(frac{2pi}{3}) = -frac{1}{2}$.
Answer 3
Abigail Nelson
What is the value of $cos(pi)$ on the unit circle?
At an angle of $pi$, which is 180 degrees, the coordinates on the unit circle are $(-1, 0)$.
Therefore, the cosine of $pi$ is $cos(pi) = -1$.
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