What is the cosine and sine of the angle $frac{pi}{4}$ on the unit circle?
Answer 1
Ava Martin
To find the cosine and sine of the angle $\frac{\pi}{4}$ on the unit circle, we need to recall the coordinates of the point where the terminal side of the angle intersects the unit circle.
For the angle $\frac{\pi}{4}$, both the x-coordinate (cosine) and y-coordinate (sine) are equal. Since the unit circle has a radius of 1, we use the fact that $\cos(\theta) = \sin(\theta) = \frac{\sqrt{2}}{2}$ for this specific angle. Therefore,
$\cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$
$\sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$
Answer 2
Joseph Robinson
On the unit circle, the coordinates of the points are given by $ (cos( heta), sin( heta)) $ for an angle $ heta $.
Given $ heta = frac{pi}{4} $, we look for the coordinates of this angle. It is known that at $ frac{pi}{4} $, the coordinates are $ left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $.
Therefore:
$cosleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2}$
$sinleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2}$
Answer 3
John Anderson
The cosine and sine of the angle $frac{pi}{4}$ on the unit circle are:
$cosleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2}$
$sinleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2}$
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