The tan inverse of 1, often written as arctan(1) or tan-1(1), is equal to π/4 radians.
In other words, if tan(x) = 1, then x = π/4 + nπ, where n is an integer. The principal value (the most common answer) is π/4.
- Explanation: The tangent function gives a value of 1 at an angle of 45 degrees. In radians, 45 degrees is equivalent to π/4.
- General Solution: While π/4 is the principal value, the tangent function repeats every π radians. Therefore, the general solution is x = π/4 + nπ, where 'n' is any integer (..., -2, -1, 0, 1, 2, ...). This means that tan(π/4), tan(5π/4), tan(9π/4), etc., all equal 1.
- Principal Value Focus: When someone asks "What is the tan inverse of 1?", they are generally looking for the principal value, which is π/4.
