Is $\cos(x) \geq 1 - \frac{x^2}{2}$ for all $x$ in $R$? I encountered this question:
Is $\cos(x) \geq 1 - \frac{x^2}{2}$   for all $x$ in  $R$  ?
I draw to myself the function graphs but i can't find the right way to answer this type of questions.
Cosx function graph
1-x^2/2 function graph

Another method is using the well known inequality $\sin { x\le x } $ and integrating both sides $$\int _{ 0 }^{ x }{ \sin { tdt\le \int _{ 0 }^{ x }{ tdt }  }  } $$ 
$${ \cos { t } | }_{ 0 }^{ x }\le { \frac { { t }^{ 2 } }{ 2 } | }_{ 0 }^{ x }$$
$$-\cos { x } +1\le \frac { { x }^{ 2 } }{ 2 } \\$$

$$ \cos { x } \ge 1-\frac { { x }^{ 2 } }{ 2 } $$

