Calculate the values of $ an(pi/4)$, $ an(pi/6)$, and $ an(pi/3)$ using the unit circle.

Let’s calculate the values of $\tan(\pi/4)$, $\tan(\pi/6)$, and $\tan(\pi/3)$ using the unit circle:

1. $\tan(\pi/4)$:

On the unit circle, the angle $\pi/4$ (45 degrees) corresponds to the point $(\sqrt{2}/2, \sqrt{2}/2)$. The tangent function is defined as $\tan(\theta) = \frac{y}{x}$.

Therefore,

$\tan(\pi/4) = \frac{\sqrt{2}/2}{\sqrt{2}/2} = 1$

2. $\tan(\pi/6)$:

On the unit circle, the angle $\pi/6$ (30 degrees) corresponds to the point $(\sqrt{3}/2, 1/2)$. Therefore,

$\tan(\pi/6) = \frac{1/2}{\sqrt{3}/2} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$

3. $\tan(\pi/3)$:

On the unit circle, the angle $\pi/3$ (60 degrees) corresponds to the point $(1/2, \sqrt{3}/2)$. Therefore,

$\tan(\pi/3) = \frac{\sqrt{3}/2}{1/2} = \sqrt{3}$

To find the values of $ an(pi/4)$, $ an(pi/6)$, and $ an(pi/3)$ using unit circle:

1. $ an(pi/4)$:

From the unit circle, $pi/4$ corresponds to $(sqrt{2}/2, sqrt{2}/2)$.

$ an(pi/4) = frac{sqrt{2}/2}{sqrt{2}/2} = 1$

2. $ an(pi/6)$:

From the unit circle, $pi/6$ corresponds to $(sqrt{3}/2, 1/2)$.

$ an(pi/6) = frac{1/2}{sqrt{3}/2} = frac{1}{sqrt{3}} = frac{sqrt{3}}{3}$

3. $ an(pi/3)$:

From the unit circle, $pi/3$ corresponds to $(1/2, sqrt{3}/2)$.

$ an(pi/3) = frac{sqrt{3}/2}{1/2} = sqrt{3}$

Calculate $ an(pi/4)$, $ an(pi/6)$, and $ an(pi/3)$:

1. $ an(pi/4) = 1$

2. $ an(pi/6) = frac{sqrt{3}}{3}$

3. $ an(pi/3) = sqrt{3}$

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