Yes, the arctan (inverse tangent) function essentially cancels out the tangent function, but with some important details to keep in mind.
When you apply the arctan function to a value, you are looking for the angle whose tangent is that value. In mathematical terms, if you have a tangent value ‘x’, then:
arctan(tan(θ)) = θ for any angle θ in the range -π/2 < θ < π/2.
However, it’s crucial to understand the limitations. The output of the arctan function is restricted to angles between -90° and 90° (or -π/2 and π/2 radians). This means that if you input a tangent value that corresponds to an angle outside this range, applying arctan to the output of the tangent function will not yield the original angle. For instance:
tan(π/4) = 1, so arctan(1) = π/4. This holds true. But if you evaluate:
tan(3π/4) = -1, you would find arctan(-1) = -π/4, which does not equal 3π/4.
In summary, while arctan does