The inverse tangent function, tan^(-1)(x), also known as arctan(x), is used to obtain an angle whose tangent is x.

Here, we are asked to find the exact value of tan^(-1)(-1).

We know that tan(θ) = -1 when θ = -π/4 or θ = 3π/4 in the standard [-π/2, π/2] range for the inverse tangent function.

However, since the range of arctan(x) or tan^(-1)(x) is (-π/2, π/2), the value of θ = 3π/4 is not in the valid range.

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

Question

The inverse tangent function, tan^(-1)(x), also known as arctan(x), is used to obtain an angle whose tangent is x.

Here, we are asked to find the exact value of tan^(-1)(-1).

We know that tan(θ) = -1 when θ = -π/4 or θ = 3π/4 in the standard [-π/2, π/2] range for the inverse tangent function.

However, since the range of arctan(x) or tan^(-1)(x) is (-π/2, π/2), the value of θ = 3π/4 is not in the valid range.

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

Knowee AI · Accepted Answer

The inverse tangent function, tan^(-1)(x), also known as arctan(x), is used to obtain an angle whose tangent is x.

Here, we are asked to find the exact value of tan^(-1)(-1).

We know that tan(θ) = -1 when θ = -π/4 or θ = 3π/4 in the standard [-π/2, π/2] range for the inverse tangent function.

However, since the range of arctan(x) or tan^(-1)(x) is (-π/2, π/2), the value of θ = 3π/4 is not in the valid range.

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

Find the exact value of tan−1−1.Write your answer in radians in terms of π.