What is Cotangent
Let a right-angled triangle ABC with an acute angle α be given, then the cotangent of angle α will be the ratio of
the adjacent leg to the opposite one cot α = AB/BC .
The cotangent of an angle can be defined as the ratio of the cosine of an angle to the sine of a given angle
cot α = cos α/sin α
You can also use a circle constructed in a Cartesian coordinate system, radius R and center at the origin O to determine the cotangent of an angle.
On the circle, mark the point P with coordinates (1; 0), now turn the ray OP by some angle α.
Counterclockwise direction is considered positive, clockwise direction is negative.
The cotangent of angle α will be the ratio of the abscissa of point XP to the ordinate of point YP.
cot α = XP/YP.
To calculate the cotangent of an angle, you can also use the cotangent axis. Let us define a circle of radius R as a unit circle centered at the origin O.
Parallel to the x axis, at a distance equal to the radius of the circle, we place the straight line y = 1. On the circle, mark the point P with coordinates (1; 0),
now turn the ray OP by some angle α and extend the ray OP to the intersection with the line y = 1.
The cotangent of angle α will correspond to the value at point B .