Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. the angle 60° is shown below in standard position, together with a unit circle. use the coordinates of the point of intersection of the terminal side and the circle to compute tan 60°. $\frac{sqrt{3}}{2}$ $\frac{sqrt{3}}{3}$ $\frac{1}{2}$ $sqrt{3}$

Explanation:

Step1: Recall tangent formula

The formula for the tangent of an angle $\theta$ in the unit - circle is $\tan\theta=\frac{y}{x}$, where $(x,y)$ are the coordinates of the point of intersection of the terminal side of the angle $\theta$ and the unit - circle.

Step2: Identify coordinates

For a $60^{\circ}$ angle in standard position, the coordinates of the point of intersection of the terminal side and the unit - circle are $x = \frac{1}{2}$ and $y=\frac{\sqrt{3}}{2}$.

Step3: Calculate tangent value

Substitute $x=\frac{1}{2}$ and $y = \frac{\sqrt{3}}{2}$ into the tangent formula: $\tan60^{\circ}=\frac{y}{x}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\sqrt{3}$.

Answer:

$\sqrt{3}$