Find the $sin$, $cos$, and $ an$ of $45^circ$ on the unit circle.
Answer 1
Daniel Carter
We know that at $45^\circ$, the coordinates on the unit circle are $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$.
Therefore,
$\sin 45^\circ = \frac{\sqrt{2}}{2}$
$\cos 45^\circ = \frac{\sqrt{2}}{2}$
To find $\tan 45^\circ$, we use the identity $\tan \theta = \frac{\sin \theta}{\cos \theta}$:
$\tan 45^\circ = \frac{\sin 45^\circ}{\cos 45^\circ} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$
Answer 2
Sophia Williams
The position on the unit circle corresponding to $45^circ$ is $left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
Thus,
$sin 45^circ = frac{sqrt{2}}{2}$
$cos 45^circ = frac{sqrt{2}}{2}$
For $ an 45^circ$, we apply $ an heta = frac{sin heta}{cos heta}$:
$ an 45^circ = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1$
Answer 3
Emily Hall
At $45^circ$ on the unit circle, the coordinates are $left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$.
Therefore,
$sin 45^circ = frac{sqrt{2}}{2}$
$cos 45^circ = frac{sqrt{2}}{2}$
$ an 45^circ = 1$
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