What is the cosine of the angle $45^circ$ on the unit circle?
Answer 1
Chloe Evans
The angle 45 degrees is equivalent to $\frac{\pi}{4}$ radians.
On the unit circle, the coordinates for an angle of $45^\circ$ or $\frac{\pi}{4}$ radians are $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$.
Thus, the cosine of $45^\circ$ is $\frac{\sqrt{2}}{2}$.
$ \cos 45^\circ = \frac{\sqrt{2}}{2} $
Answer 2
Michael Moore
First, convert 45 degrees to radians: $45^circ = frac{pi}{4}$ radians.
Recall that on the unit circle, the x-coordinate of a point gives the cosine of the angle.
For $frac{pi}{4}$ radians, the coordinates are $(frac{sqrt{2}}{2}, frac{sqrt{2}}{2})$.
Therefore, the cosine of $frac{pi}{4}$ is $frac{sqrt{2}}{2}$.
$ cos frac{pi}{4} = frac{sqrt{2}}{2} $
Answer 3
Christopher Garcia
The angle $45^circ$ equals $frac{pi}{4}$ radians.
On the unit circle, the cosine of $frac{pi}{4}$ is $frac{sqrt{2}}{2}$.
$ cos frac{pi}{4} = frac{sqrt{2}}{2} $
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