Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

4 years ago I have not been in sight for a math book. Today I had a dumb question. I hope you can understand me.

$(\sin(x))^2$ is $\sin(x^2)$ or $\sin^2(x)$

I believe that to learn calculus, the first thing I have to do is accept that I have difficulties in basic areas such as trigonometry.

share|improve this question
    
The second one. –  ՃՃՃ Nov 10 '12 at 4:40
    
The second one? –  Rakisbro Nov 10 '12 at 4:43
    
Yes.${}{}{}{}{}$ –  ՃՃՃ Nov 10 '12 at 4:45

3 Answers 3

up vote 4 down vote accepted

$(f(x))^2$ is often written as $f^2(x)$ and in general, $(f(x))^2\ne f(x^2)$

Example, $(\sin x)^2=\sin^2x, (\cosh x)^2=\cosh^2x, (\log x)^2=\log^2x$

Of course, in many functions like Algebraic/Polynomial ones, $f(x)=ax^2+bx+c$ this notation does not make sense.

share|improve this answer
    
You answer is all. thanks –  Rakisbro Nov 10 '12 at 4:45
    
@Rakisbro, welcome anytime. –  lab bhattacharjee Nov 10 '12 at 4:46
    
This notation isn't generally understood to have the same meaning unless the function is trigonometric. –  Dan Brumleve Nov 10 '12 at 6:51
    
@DanBrumleve, is that the reason for down-voting? It's too obvious that we can't use this notation for Algebraic/Polynomial/Exponential/Logarithmic Function unlike for Trigonometric/Hyperbolic. –  lab bhattacharjee Nov 10 '12 at 8:41
2  
Yes. Why is it obvious that $\tan^2{x}$ should mean $(\tan{x})^2$ but $\log^2{x}$ should mean something else? I explained my opinion in my own answer. –  Dan Brumleve Nov 10 '12 at 8:46

With trigonometric functions, such as $y= \tan(x)$, it is standard to write $$y^2=\tan^2(x)$$

share|improve this answer

As Linear Man says, this is a common notation for trigonometric functions. However, in a more general context, $f^2(x)$ may mean $f(f(x))$ rather than $(f(x))^2$ as lab bhattacharjee claims. I think it is a poor notation for any other meaning even when limited to trigonometric functions and I prefer to write $(\sin{x})^2$ or $\sin{(x)}^2$ when I mean that, and I am quite comfortable with $\sin^2{(x)}$ or even $\sin^2{x}$ as a notation for $\sin{(\sin{(x)})}$ or with equivalent unambiguity $\sin{\sin{x}}$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.