tan^2(x)

  • iochinome
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Post 3+ Months Ago

hey guys, i am doing math hw and i just came accross something that is asking wether tan^2(x) = tan[(x)^2], which might be doable if i knew what tan^2 meant. anybody? thanks
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Post 3+ Months Ago

I think it means tangent squared if I remember my trig. But don't count on that. I got a C in Trig.
  • iochinome
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Post 3+ Months Ago

oh so its just the same as tan(x)^2?
  • spork
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Post 3+ Months Ago

Yes.

tan^2(x) means take the tangent of x, and square the result.

tan(x^2) means square x, then take the tangent of the result.
  • neksus
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Post 3+ Months Ago

The ^ usually refers to powers, so tan^2 would be tan squared.
  • SpooF
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Post 3+ Months Ago

Yep, heres another way of writing the problem out, this might help.

[tan(x)]^2 = tan([x^2])
  • spork
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Post 3+ Months Ago

Ah, the dark ages of trig and calculus... before mankind was enlightened in the ways of true mathematics: discrete mathematics.
  • iochinome
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Post 3+ Months Ago

so anyone wanna give a whack at it, see if its true? because i know i dont!
  • spork
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Post 3+ Months Ago

Ain't doing your homework for ya pal ;)

Is it really that hard to plug in a value for x and see if it holds true or not?
  • iochinome
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Post 3+ Months Ago

thats not the point of the homework though... it might be easy but im looking for a more proof-oriented look at it. plus, there is probably some number that it holds true for, so i could never swing that answer with my math teacher.
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Post 3+ Months Ago

If you're trying to prove something to be false, then finding just one counterexample is usually enough proof in a situation like this. You just can't prove it to be true by an example.

But if you do need to write out a proof, then start by thinking of trig identities that you can use to rework the problem into a more obvious one.
  • iochinome
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Post 3+ Months Ago

ok thanks
  • neksus
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Post 3+ Months Ago

I miss calculus :(
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Post 3+ Months Ago

spork wrote:
Ah, the dark ages of trig and calculus... before mankind was enlightened in the ways of true mathematics: discrete mathematics.



And scientific calculators.
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Post 3+ Months Ago

neksus wrote:
I miss calculus :(


I don't :( my calc teacher is giving my class tests all this week and next, practice AP test, to bad they are graded ><
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Post 3+ Months Ago

Whoa, i think i've come across the first ever post on Ozzu where i genuinely think you are all typing a load of gibberish.

I never liked mathematics*.


*i say mathematics because i know some people prefer to call it "math" and others call it "maths".
  • spork
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Post 3+ Months Ago

Simply put, your opinion is wrong. :)
  • neksus
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Post 3+ Months Ago

Mathematics was always my favourite class :)
An inherent ability never hurts though.

I memorized Pi to 100 digits because I refused to use a calculator during that class (Logs kicked my ass though). I got sick of people whipping them out to figure out 3x21 :P
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Post 3+ Months Ago

iochinome wrote:
hey guys, i am doing math hw and i just came accross something that is asking wether tan^2(x) = tan[(x)^2], which might be doable if i knew what tan^2 meant. anybody? thanks


[tex]Tan^2(x) = tan(x) * tan(x)[/tex]
[tex]tanx^2 = tan (x^2)[/tex]

Those two are different! One represents the 2nd power of the tangent function, and the other is the 2nd power of the argument x!

It' s the same explination like in [tex]f(x^2) and f^2(x)[/tex]. You cannot put "=" between them.

I' ll give you a short example: let x be 1. => [tex]tan^2(1) = tan(1) * tan(1)[/tex]
[tex]tan(1^2) = tan(1).[/tex]

So for what you' re saying, those two should be equivalent:
[tex]tan(1)*tan(1) = tan(1).[/tex] By dividing with tan(1) that is not null => tan(1) = 1. This is false.

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