What is the inverse trig function cotangent of square root of 3/3? What is the value?

60 degrees

Thanks.

To find the inverse trig function of cotangent, we need to understand its definition. The cotangent (cot) function is the reciprocal of the tangent (tan) function. So, if we find the tangent of an angle, we can then take the reciprocal to find the cotangent.

Let's start by finding the tangent of an angle with the value √3/3. We can use the formula tan(x) = opposite/adjacent in a right triangle to find the tangent.

Given that the adjacent side is √3 and the opposite side is 1 (since √3/3 = 1/√3), we can define the tangent as tan(x) = opposite/adjacent = 1/√3.

To find the value of the angle, we need to take the inverse tangent (arctan) of 1/√3. This will give us the measure of the angle itself.

The equation to find the inverse tangent is arctan(y) = x, where y is the value we want to find the inverse tangent of, and x is the angle measure.

Therefore, arctan(1/√3) = x.

To evaluate this, we can use a calculator or a table of trigonometric values. The value of arctan(1/√3) is approximately 30 degrees or π/6 in radians.

Finally, since the cotangent (cot) is the reciprocal of the tangent (tan), we can find cot(π/6) by taking the reciprocal of tan(π/6).

cot(π/6) = 1/tan(π/6) = 1/√3.

So, the value of the inverse trig function cot(√3/3) is 1/√3.