Find the sine and cosine values of the angle $ heta = frac{pi}{4}$ on the unit circle.
Answer 1
Isabella Walker
To find the sine and cosine values for $\theta = \frac{\pi}{4}$, we refer to the unit circle.
On the unit circle, the coordinates of the point corresponding to $\theta = \frac{\pi}{4}$ are $\left( \cos \frac{\pi}{4}, \sin \frac{\pi}{4} \right)$.
Since $\frac{\pi}{4}$ is a commonly known angle, we know that:
$\cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}$
$\sin \frac{\pi}{4} = \frac{\sqrt{2}}{2}$
Therefore, the sine and cosine values for $\theta = \frac{\pi}{4}$ are both $\frac{\sqrt{2}}{2}$.
Answer 2
Joseph Robinson
To determine the sine and cosine of $ heta = frac{pi}{4}$ on the unit circle, we look at the point where the terminal side of the angle intersects the unit circle.
At $ heta = frac{pi}{4}$, this point is $left( cos frac{pi}{4}, sin frac{pi}{4}
ight)$.
From basic trigonometric identities, we know:
$cos frac{pi}{4} = frac{sqrt{2}}{2}$
$sin frac{pi}{4} = frac{sqrt{2}}{2}$
Thus, the values are $cos frac{pi}{4} = frac{sqrt{2}}{2}$ and $sin frac{pi}{4} = frac{sqrt{2}}{2}$.
Answer 3
John Anderson
For $ heta = frac{pi}{4}$ on the unit circle:
$cos frac{pi}{4} = frac{sqrt{2}}{2}$
$sin frac{pi}{4} = frac{sqrt{2}}{2}$
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