What is the value of $ sin(frac{pi}{4}) $ using the unit circle?
Answer 1
Matthew Carter
To find the value of $ \sin(\frac{\pi}{4}) $ using the unit circle, we need to identify the coordinates of the point on the unit circle corresponding to $ \frac{\pi}{4} $ radians.
The angle $ \frac{\pi}{4} $ radians is equivalent to 45 degrees. On the unit circle, the coordinates of the point that corresponds to 45 degrees are $ (\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}) $.
Since $ \sin(\theta) $ is equal to the y-coordinate of the point on the unit circle, we have
$ \sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2} $
Answer 2
Ella Lewis
To determine $ sin(frac{pi}{4}) $ using the unit circle, we need to find the point on the circle that corresponds to an angle of $ frac{pi}{4} $ radians.
The angle $ frac{pi}{4} $ radians is also known as 45 degrees. The coordinates of the point on the unit circle at this angle are $ (frac{sqrt{2}}{2}, frac{sqrt{2}}{2}) $.
Therefore, the value of $ sin(frac{pi}{4}) $ is the y-coordinate of this point:
$ sin(frac{pi}{4}) = frac{sqrt{2}}{2} $
Answer 3
Lily Perez
To find $ sin(frac{pi}{4}) $ using the unit circle, identify the coordinates of the point on the circle at $ frac{pi}{4} $ radians.
The coordinates at $ frac{pi}{4} $ radians are $ (frac{sqrt{2}}{2}, frac{sqrt{2}}{2}) $.
Thus,
$ sin(frac{pi}{4}) = frac{sqrt{2}}{2} $
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