how is cot pi over 3 is root3?

Answer 1

The value of cot(pi/3) is equal to the reciprocal of the tangent of pi/3.

The tangent of pi/3 is √3 because in a unit circle, at an angle of pi/3, the y-coordinate of the point on the unit circle is 1/2, and the x-coordinate is √3/2. Therefore, the tangent is √3/1/2 = √3.

Since the cotangent is the reciprocal of the tangent, cot(pi/3) = 1/√3. Rationalizing the denominator by multiplying the numerator and denominator by √3, we get √3/√3*√3 = √3/3.

Therefore, cot(pi/3) is equal to √3/3 or root 3/3.