|sin a|<=a

[Guest]

Can anyone prove this?
|sin a|<=a
I have a test tomorrow

[Guest]

Can anyone prove this?
|sin a|<=|a|
I have a test tomorrow[/quote]

[Guest]

Can anyone prove this?

It Is need to prove that this Is the true for every x

|sin a|<=a


I have a test tomorrow

[Guest]

This is obviously NOT true! If x< 0, |sin(x)| is positive so x< |sin(x)|.

[Guest]

[tex]|sin\alpha| \le| \alpha|[/tex]
[tex]\forall \alpha \in R[/tex]
[tex]\alpha \in(- \infty,-1][/tex]
[tex]|sin\alpha| \le 1[/tex]
[tex]|\alpha|=-\alpha \ge1[/tex]
[tex]|sin\alpha| \le| \alpha|[/tex]
[tex]\alpha \in(-1,0)[/tex]
[tex]\alpha < \beta < 0[/tex]
[tex](sin\beta)'=(sin\alpha-sin0)/(\alpha-0)[/tex]
[tex]cos\beta=sin\alpha/\alpha[/tex]
[tex]cos\beta\le1[/tex]
[tex]sin\alpha/\alpha\le1[/tex]
[tex](sin\alpha/\alpha) \cdot (-1)\cdot\alpha\le1 \cdot(-1)\cdot\alpha[/tex]
[tex](-1)\cdot sin\alpha \le (-1)\cdot\alpha[/tex]
[tex]|sin\alpha| \le |\alpha|[/tex]
[tex]\alpha=0[/tex]
[tex]|\sin0|=|0|=0 \le0=|0|[/tex]
[tex]|sin\alpha| \le |\alpha|[/tex]
[tex]\alpha \in(0,1)[/tex]
[tex]0< \beta < \alpha[/tex]
[tex](sin\beta)'=(sin0-sin\alpha)/(0-\alpha)[/tex]
[tex]cos\beta= sin\alpha/\alpha[/tex]
[tex]cos\beta\le1[/tex]
[tex]sin\alpha/\alpha\le1[/tex]
[tex](sin\alpha/\alpha) \cdot\alpha\le1\cdot\alpha[/tex]
[tex]sin\alpha \le \alpha[/tex]
[tex]|sin\alpha| \le |\alpha|[/tex]
[tex]\alpha \in[1, \infty)[/tex]
[tex]|sin\alpha| \le 1[/tex]
[tex]|\alpha|=\alpha \ge1[/tex]
[tex]|sin\alpha| \le| \alpha|[/tex]