Find the sine and cosine of $45^{circ}$ using the unit circle.
Answer 1
Ava Martin
To find the sine and cosine of $45^{\circ}$ using the unit circle, we need to locate $45^{\circ}$ on the unit circle chart.
The coordinates of the point where the $45^{\circ}$ angle intersects the unit circle are $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$.
Thus, the sine of $45^{\circ}$ is the y-coordinate:
$\sin(45^{\circ}) = \frac{\sqrt{2}}{2}$
And the cosine of $45^{\circ}$ is the x-coordinate:
$\cos(45^{\circ}) = \frac{\sqrt{2}}{2}$
Answer 2
Chloe Evans
First, we identify the $45^{circ}$ angle on the unit circle. The unit circle has the property that any angle’s coordinates are $(cos( heta), sin( heta))$.
For $45^{circ}$, we find that the coordinates are $(frac{sqrt{2}}{2}, frac{sqrt{2}}{2})$.
Therefore,
$sin(45^{circ}) = frac{sqrt{2}}{2}$
and
$cos(45^{circ}) = frac{sqrt{2}}{2}$
Answer 3
Charlotte Davis
For $45^{circ}$ on the unit circle, the coordinates are $(frac{sqrt{2}}{2}, frac{sqrt{2}}{2})$.
So,
$sin(45^{circ}) = frac{sqrt{2}}{2}$
$cos(45^{circ}) = frac{sqrt{2}}{2}$
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