Sin x^2, Sin^2 x, (Sinx)^2

Date: 09/12/2001 at 09:51:32
From: Rob
Subject: Sin

What is the difference between sin x^2, sin^2 x, and (sinx)^2?

Date: 09/12/2001 at 10:47:22
From: Doctor Ian
Subject: Re: Sin

Hi Rob,

Suppose x = pi/6, which means that sin x = 1/2.  Then

  1. sin x^2 = sin ((pi/6)^2)

             = sin (pi^2/36)

  2. sin^2 x = (sin pi/4)^2

             = (1/2)^2

             = 1/4

  3. (sin x)^2 = sin^2 x   

It would seem pretty natural to think that

  sin^2 x = sin(sin x)

but this isn't the convention that's been adopted. 
  
Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/