# Homework Help: Calc Help

1. Apr 18, 2005

### maverick280857

Hi

This is a fairly straightforward problem but I want to do it using calculus. Here goes:

Prove that $\sin 1 > \cos(\sin 1)$.

This is what I've done (I've hardly done much):

Let $f(x) = \sin(\cos(\sin x) - \cos(\sin(\cos(x)))$. I also have to show that f(x) = 0 has exactly one solution in $[0,\pi/2]$. So anyway, f'(x) < 0 for all x in this interval which in particular means that f(0) > f($\pi/2$). But the first part requires showing that f(0) > 0. Can this be done by a purely calculus-based argument? It is easily done if we bend the inequality a bit and observe that it is true if $\pi/2 -1 <\sin 1$.

Thanks and cheers
Vivek

2. Apr 21, 2005

### maverick280857

Hi all

This was buried deep inside the forum and I had to fish it out. Just a reminder asking for help with it...

Thanks and cheers
Vivek