Answer:
[tex]tan(\theta )=\sqrt{3}/3[/tex]
Explanation:
Tangent trigonometric ratio is defined as the quotient of the opposite leg divided by the adjacent leg of an angle in a right triangle.
In a unit circle, the length of the opposite leg is the y-coordinate and the length of the adjacent leg is the x-coordinate.
As per the description the radius goies to point:
[tex](\frac{\sqrt{3} }{2},\frac{1}{2})[/tex]
Thus, the tangent is:
[tex]tan(\theta )=y/x=(1/2)/(\sqrt{3}/2)=\sqrt{3}/3[/tex]
Using the unit circle, it is found that:
[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]
In this problem, the point is:
[tex](\cos{\theta}, \sin{\theta}) = \left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)[/tex]
Hence, the tangent is:
[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}[/tex]
To learn more about the unit circle, you can take a look at https://brainly.com/question/16852127
