Oldos, there are at LEAST 3 things
Thinking I know the general idea
Thinking I know exactly (definition)
Thinking I understand
For me the general idea is all I can ever hope for and I genuinely believe that ONLY EXAMPLES teach us anything at all! It's how we learned to walk; how we learned to talk.
An easy way to get the general idea comes in two steps
(a) Draw a triangle and POINT OUT which two sides have length-ratio that equals "tangent" and which ANGLE it is the tangent of.
(b) REMEMBER, from your experience so far, that it is USEFUL to have things "the other way round".
For example if you know y only when we know x, then the "other way round" is useful when we DO KNOW y but want to know x. For example when y=x+4 then x=y-4 "turns it around"
When y=x squared, then x=sqrt(y). When y= tan(x) then x= atn(y)
AFTER I get the general idea, THEN is the time to think whether atn might have MANY values for each given y
With complete respect, Oldos, the definition woun't help you at all.
For what you want is a rough definition and maths folk have no interest in helping you find that.
They will tell you that tan(x) = [exp(ix)-exp(-ix)]/[i*(exp(ix)+exp(-ix))]
and yes, "turn that around to give x" and you get logarithms
Clippy's tangent is a good way, but suffers from the fact that to "see what" tangent is you have to see what BOTH sine and cosine are before "dividing one by the other" is much help!