What is the value of $sin(frac{pi}{4})$ and $cos(frac{pi}{4})$ on the unit circle?
Answer 1
Ava Martin
To find the values of $\sin(\frac{\pi}{4})$ and $\cos(\frac{\pi}{4})$ on the unit circle, we use the coordinates of the point on the unit circle corresponding to the angle $\frac{\pi}{4}$.
The angle $\frac{\pi}{4}$ radians corresponds to 45 degrees. On the unit circle, the coordinates of this angle are $\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$.
Therefore, $\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ and $\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$
Answer 2
Chloe Evans
To determine the values of $sin(frac{pi}{4})$ and $cos(frac{pi}{4})$ on the unit circle, note that $frac{pi}{4}$ radians is the same as 45 degrees.
In a 45-degree angle on the unit circle, both sine and cosine values are the same due to the symmetry of the unit circle.
The coordinates are $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$, hence $sin(frac{pi}{4}) = frac{sqrt{2}}{2}$ and $cos(frac{pi}{4}) = frac{sqrt{2}}{2}$
Answer 3
Charlotte Davis
The angle $frac{pi}{4}$ radians on the unit circle corresponds to the point $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
Thus, $sin(frac{pi}{4}) = frac{sqrt{2}}{2}$ and $cos(frac{pi}{4}) = frac{sqrt{2}}{2}$
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