Cotangent: in a Right Triangle
How to find cotangent in a right triangle (trigonometry): formula, 1 example, and its solution.
Formula
Formula
Cotangent is the reciprocal of tangent.
So, to find cotangent (cot A),
first write 1/[tan A],
find tan A = (Opposite side)/(Adjacent side),
and write the reciprocal of tan A:
1 / [(Opposite side)/(Adjacent side)].
Example
Example
Solution
Cotangent is the reciprocal of tangent.
And tangent is TOA:
Tangent, Opposite side, Adjacent side.
But the side adjacent to ∠A is unknown.
So set the adjacent side x
and find x first.
The given triangle is a right triangle.
So, by the Pythagorean theorem,
x2 + 22 = 52.
+22 = +4
52 = 25
Move +4 to the right side.
Then x2 = 21.
Square root both sides.
Then x = √21.
x is the adjacent side.
So x is plus.
So you don't have to write ±.
Write √21
below the adjacent side.
cot A = 1/[tan A]
Find tan A.
Tangent is TOA:
Tangent,
Opposite side (2),
Adjacent side (√21).
So 1/[tan A] = 1/[2/√21].
1/[2/√21] = √21/2
The reciprocal of 2/√21 is
√21/2.
So cot A = √21/2.