Find the sine and cosine of the angle $ heta = 45°$ using the unit circle.
Answer 1
James Taylor
To find the sine and cosine of the angle $\theta = 45°$, we use the unit circle where the radius is 1.
The coordinates of the point where the terminal side of a 45° angle intersects the unit circle are $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$.
Therefore, $\cos(45°) = \frac{\sqrt{2}}{2}$ and $\sin(45°) = \frac{\sqrt{2}}{2}$.
Answer 2
Michael Moore
Using the unit circle, the angle $ heta = 45°$ corresponds to a point whose coordinates are $left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
Since the x-coordinate represents the cosine and the y-coordinate represents the sine: $cos(45°) = frac{sqrt{2}}{2}$ and $sin(45°) = frac{sqrt{2}}{2}$.
Answer 3
Christopher Garcia
On the unit circle, the angle $ heta = 45°$ intersects at $left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$. Thus, $cos(45°) = frac{sqrt{2}}{2}$ and $sin(45°) = frac{sqrt{2}}{2}$.
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