Determine the $ an$ values of specific angles on the unit circle
Answer 1
Lily Perez
We need to determine the $\tan$ values for the angles $30^{\circ}$, $45^{\circ}$, and $60^{\circ}$ on the unit circle:
1. For $30^{\circ}$:
$\tan 30^{\circ} = \frac{\sin 30^{\circ}}{\cos 30^{\circ}} = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$
2. For $45^{\circ}$:
$\tan 45^{\circ} = \frac{\sin 45^{\circ}}{\cos 45^{\circ}} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$
3. For $60^{\circ}$:
$\tan 60^{\circ} = \frac{\sin 60^{\circ}}{\cos 60^{\circ}} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \sqrt{3}$
Answer 2
Matthew Carter
To find the $ an$ values for the angles $30^{circ}$, $45^{circ}$, and $60^{circ}$ on the unit circle, we use the definitions of sine and cosine:
1. For $30^{circ}$:
$ an 30^{circ} = frac{sin 30^{circ}}{cos 30^{circ}} = frac{1/2}{sqrt{3}/2} = frac{1}{sqrt{3}} = frac{sqrt{3}}{3}$
2. For $45^{circ}$:
$ an 45^{circ} = frac{sin 45^{circ}}{cos 45^{circ}} = frac{sqrt{2}/2}{sqrt{2}/2} = 1$
$ an 60^{circ} = frac{sin 60^{circ}}{cos 60^{circ}} = frac{sqrt{3}/2}{1/2} = sqrt{3}$
Answer 3
Abigail Nelson
Finding $ an$ values for $30^{circ}$, $45^{circ}$, and $60^{circ}$:
$ an 30^{circ} = frac{1/2}{sqrt{3}/2} = frac{1}{sqrt{3}} = frac{sqrt{3}}{3}$
$ an 45^{circ} = frac{sqrt{2}/2}{sqrt{2}/2} = 1$
$ an 60^{circ} = frac{sqrt{3}/2}{1/2} = sqrt{3}$
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