Find the exact value of tan−1tan−6π5.Write your answer in radians in terms of π.If necessary, click on "Undefined."

The problem is asking for the exact value of tan^(-1)(tan(-6π/5)).

Step 1: Understand the problem The inverse tangent function, tan^(-1), is the inverse of the tangent function. It undoes the action of the tangent function. So, if we have tan^(-1)(tan(x)), the result is x, as long as x is within the range of the inverse tangent function. The range of the inverse tangent function is (-π/2, π/2).

Step 2: Check if the value is within the range The value -6π/5 is not within the range of the inverse tangent function.

Step 3: Adjust the value to fit within the range We can add or subtract multiples of π to bring the value within the range. In this case, we can add 2π to -6π/5 to get a value within the range.

-6π/5 + 2π = -6π/5 + 10π/5 = 4π/5

Step 4: Substitute the adjusted value back into the original problem So, tan^(-1)(tan(-6π/5)) = tan^(-1)(tan(4π/5)) = 4π/5

So, the exact value of tan^(-1)(tan(-6π/5)) is 4π/5.