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.
To find cot 60, we first need to find the x and y coordinates of the point of intersection.
From the given information, we have:
x = 1/2
y = sqrt(3)/2
Now, cot 60 is equal to adjacent over opposite. In this case, the adjacent side is x and the opposite side is y. Therefore, cot 60 can be calculated as follows:
cot 60 = x/y = (1/2) / (sqrt(3)/2) = 1/sqrt(3) = sqrt(3)/3
So, cot 60 is equal to sqrt(3)/3.