Question

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 cot 60°. 1/2 √3 √3/3 2√3/3

Explanation:

Step1: Recall cotangent formula

The formula for $\cot\theta=\frac{x}{y}$ in the unit - circle, 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 60°

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

Step3: Calculate cotangent

Substitute $x$ and $y$ into the cotangent formula: $\cot60^{\circ}=\frac{x}{y}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}$.

Answer:

$\frac{\sqrt{3}}{3}$