Find the values of $sin(frac{pi}{4})$ and $cos(frac{pi}{4})$ using the unit circle.
Answer 1
Matthew Carter
Using the unit circle, we can find the values of $\sin(\frac{\pi}{4})$ and $\cos(\frac{\pi}{4})$ by locating the angle $\frac{\pi}{4}$ radians. This angle corresponds to a 45-degree angle in the unit circle.
At this angle, both the x-coordinate (which represents $\cos(\frac{\pi}{4})$) and the y-coordinate (which represents $\sin(\frac{\pi}{4})$) are equal to $\frac{\sqrt{2}}{2}$.
Thus,
$\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$
$\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$
Answer 2
Lucas Brown
To determine $sin(frac{pi}{4})$ and $cos(frac{pi}{4})$ using the unit circle, we look at the point on the unit circle at an angle of $frac{pi}{4}$ radians from the positive x-axis.
This angle is equivalent to 45 degrees, where the coordinates of the corresponding point on the unit circle are $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
Therefore,
$sin(frac{pi}{4}) = frac{sqrt{2}}{2}$
$cos(frac{pi}{4}) = frac{sqrt{2}}{2}$
Answer 3
Lily Perez
At $frac{pi}{4}$ radians (or 45 degrees) on the unit circle, the coordinates are $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
Thus,
$sin(frac{pi}{4}) = frac{sqrt{2}}{2}$
$cos(frac{pi}{4}) = frac{sqrt{2}}{2}$
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