Difference between tan^(-1)x and 1/tanx

I thought they were the same until today. what is the difference between them? i though anything with the power (-1) is the same as 1 over that .

Reply 1

insparato

1/tanx = cot x

tan^-1x is the inverse of tan. This is more formally known as arctan. Its a completely different to 1/tanx.

Reply 2

phys981

tan 63.4 = 2, so tan^-1( 2) = 63.4

Meanwhile 1 / tan 63.4 = 1/2 = 0.5

Don't know how else to explain it....

Reply 3

generalebriety

tan^-1 is an inverse function, defined such that tan^-1(tan(x)) = tan(tan^-1(x)) = x, for most 'useful' values of x. It is true that, say, a^-1 = 1/a, but "tan" conforms to function notation and not to standard algebraic notation. It's a shame the two overlap, but it is very standard to define a function f^-1 such that f^-1(f(x)) = f(f^-1(x)) = x. arctan is another way of writing tan^-1, but obviously you can't write 'arcf' for the inverse of f, so tan^-1 stuck for convenience.

1/tanx isn't a function. It's just 1 divided by tanx.

Reply 4

Chewwy

generalebriety

1/tanx isn't a function.

well...

Reply 5

generalebriety

chewwy

well...

Blah.

Reply 6

7589200

generalebriety

1/tanx isn't a function. It's just 1 divided by tanx.

wtf lol

Reply 7

username21537

Unparseable latex formula:

[br]\frac{1}{tan(\theta)}\ =\ cot(\theta)\\[br]tan^{-1}(\theta)\ = arctanx[br]

Where

arctan(\theta)

is the inverse function of

tan(\theta)

Reply 8

James

I'm tempted to have another rant about notation...
But I'll resist. Suffice to say:

If you mean INVERSE TAN, write ARCTAN
If you mean 1/TAN, write COT

Reply 9

generalebriety

jamesgurung

I'm tempted to have another rant about notation...
But I'll resist. Suffice to say:

If you mean INVERSE TAN, write ARCTAN
If you mean 1/TAN, write COT

Fighting a losing battle here. Besides, I don't see the problem with tan^-1x = arctanx, given that it follows standard function notation. You wouldn't dream of thinking f^-1(x) = 1/f(x), would you? And you certainly wouldn't write arcf. And if you meant 1/f, you wouldn't call it something entirely different. It's a notational inconvenience, but tan^-1 is perfectly unambiguous, given that no one uses it to mean 1/tan - they'd just write cot.