cot π/6 (30)
To find the value of cot π/6 (30), we need to understand the concept of cotangent and the angle π/6 (30 degrees)
To find the value of cot π/6 (30), we need to understand the concept of cotangent and the angle π/6 (30 degrees).
Cotangent (cot) is a trigonometric function that represents the ratio of the adjacent side to the opposite side in a right triangle. It can also be defined as the reciprocal of the tangent function. The cotangent of an angle, θ, is given by cot θ = 1/tan θ.
Now, let’s consider the angle π/6 or 30 degrees. In a right triangle with this angle, we have an adjacent side, an opposite side, and a hypotenuse. The adjacent side is the side adjacent to the angle, and the opposite side is the side opposite to the angle.
To determine the value of cot π/6 (30), we need to determine the values of the adjacent and opposite sides. In this case, we know that the angle π/6 (30 degrees) corresponds to a special right triangle called a 30-60-90 triangle.
In a 30-60-90 triangle, the ratio of the sides is:
Opposite side : Hypotenuse = 1 : 2
Adjacent side : Hypotenuse = √3 : 2
Opposite side : Adjacent side = √3 : 1
Since the cotangent is the ratio of the adjacent side to the opposite side, we have cot π/6 (30) = (√3 : 1) = √3.
Therefore, the value of cot π/6 (30) is √3.
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