Question

The angle 60
is shown below in standard position, together with a unit circle.

The image shows a unit circle and a right triangle in quadrant 1 with a 60-degree angle in standard position. The hypotenuse, which is also the terminal side of the angle, has a length of 1. The terminal side intersects the circle at (one half, the square root of 3 over 2).

Use the coordinates of the point of intersection of the terminal side and the circle to compute cot 60
.

Answer 1

For the unit-circle point (x,y) = (1/2, √3/2), cot θ = x/y. So

cot 60° = (1/2) / (√3/2) = 1/√3 = √3/3.