Can We Compound The Range?

Geometry Level 2

$| \sin x | \leq 1 \qquad \qquad | \cos x | \leq 1$

We know that for all real numbers $x$ , the inequalities above are true. What is the smallest possible value of $R$ satisfying

$| \sin x + \cos x | \leq R ?$

0

1

2

3

\sqrt { 2 }

\sqrt { 3 }