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

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  (θ being some angle) works the same way. It takes in an input angle, does something to it, and produces an output value. , on the other hand, takes that output value and turns it back into that input angle.

So, with this problem, if , feeding that x back into  would just get us the original angle back, or

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It's like discovering the answer to a puzzle. the purpose in solving an equation is to find the value or values of the variable that makes it a true statement. any value of the variable that makes the equation true is called a solution to the equation.