Question

Find the tanθ (1/2,√3/2)

√3/3
√3/2
√3

Answer 1

To find \(\tan \theta\) for the point \((\frac{1}{2}, \frac{\sqrt{3}}{2})\), we use the definition of the tangent function in terms of sine and cosine:

\[
\tan \theta = \frac{\text{opposite}}{\text{adjacent}}
\]

In the context of the unit circle, the x-coordinate corresponds to the cosine of \(\theta\) and the y-coordinate corresponds to the sine of \(\theta\). Here:

- \(\cos \theta = \frac{1}{2}\)
- \(\sin \theta = \frac{\sqrt{3}}{2}\)

Now we can compute \(\tan \theta\):

\[
\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \frac{\sqrt{3}}{2} \cdot \frac{2}{1} = \sqrt{3}
\]

Thus, the value of \(\tan \theta\) is:

\[
\sqrt{3}
\]

So the correct answer is \(\sqrt{3}\).