Calculate the tangent of an angle when given the sine and cosine values in the unit circle

To find the tangent of an angle in the unit circle when given the sine and cosine values, we use the formula:

$ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} $

For example, if $\sin(\theta) = \frac{1}{2}$ and $\cos(\theta) = \frac{\sqrt{3}}{2}$, then:

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

To calculate the tangent of an angle $ heta$ in the unit circle given the sine and cosine values, use:

$ an( heta) = frac{sin( heta)}{cos( heta)} $

For example, if $sin( heta) = 0.6$ and $cos( heta) = 0.8$, then:

$ an( heta) = frac{0.6}{0.8} = 0.75 $

Use the formula to find $ an( heta)$:

$ an( heta) = frac{sin( heta)}{cos( heta)} $

If $sin( heta) = 0.5$ and $cos( heta) = 0.5sqrt{3}$, then:

$ an( heta) = frac{0.5}{0.5sqrt{3}} = frac{1}{sqrt{3}} = frac{sqrt{3}}{3} $

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