Find the tangent values at Define the unit circle in trigonometry$, $frac{pi}{4}$, and $frac{pi}{3}$ on the unit circle

To find the tangent values at points

txt1

txt1

txt1

$, $\frac{\pi}{4}$, and $\frac{\pi}{3}$ on the unit circle, we use the tangent function $tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$:

1. At $\theta = 0$:

$ \tan(0) = \frac{\sin(0)}{\cos(0)} = \frac{0}{1} = 0 $

2. At $\theta = \frac{\pi}{4}$:

$ \tan\left(\frac{\pi}{4}\right) = \frac{\sin\left(\frac{\pi}{4}\right)}{\cos\left(\frac{\pi}{4}\right)} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1 $

3. At $\theta = \frac{\pi}{3}$:

$ \tan\left(\frac{\pi}{3}\right) = \frac{\sin\left(\frac{\pi}{3}\right)}{\cos\left(\frac{\pi}{3}\right)} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \sqrt{3} $

To find the tangent values at

txt2

txt2

txt2

$, $frac{pi}{4}$, and $frac{pi}{3}$, use $ an( heta) = frac{sin( heta)}{cos( heta)}$:

1. At

txt2

txt2

txt2

$: $ an(0) = 0$

2. At $frac{pi}{4}$: $ anleft(frac{pi}{4}
ight) = 1 $

3. At $frac{pi}{3}$: $ anleft(frac{pi}{3}
ight) = sqrt{3} $

For $ heta = 0, frac{pi}{4}, frac{pi}{3}$:

1. $ an(0) = 0 $

2. $ anleft(frac{pi}{4}
ight) = 1 $

3. $ anleft(frac{pi}{3}
ight) = sqrt{3} $

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