Question

If the tangent of ∠T is x, what is tan−1 x (the inverse tangent of x)? m∠

Answer 1

You can think of a function as some kind of machine that takes an input value, does something to it, and produces an output value. The inverse of a function flips the process around - you give it the output first, and it works in reverse to produce the original input.

The function
`tan(\theta)` (θ being some angle) works the same way. It takes in an input angle, does something to it, and produces an output value.
`\tan^(-1){x}`, on the other hand, takes that output value and turns it back into that input angle.

So, with this problem, if
`\tan{\angle{T}}=x`, feeding that x back into
`\tan^(-1)` would just get us the original angle back, or
`\tan^(-1){x}=\angle{T}`