Question

If $x=\sin 2^{\circ }$ and $y=\sin 2^c$, then the correct relation between $x$ and $y$ is

• A. $x=y$
• B. $x>y$
• C. $x<y$
• D. $x=2y$

Answer 1

The correct option is C $x<y$

$1\text{radian}={\left(\frac{180}{\pi }\right)}^{\circ }\approx {57}^{\circ }{18}^{\prime }$
$2\text{radian}\approx {115}^{\circ }$

$y=\sin 2^c\approx \sin {115}^{\circ }=\sin ({180}^{\circ }-{65}^{\circ })$
$\Rightarrow y\approx \sin {65}^{\circ }$

Since, $\sin \theta$ is increasing in $(0,\frac{\pi }{2})$
$\therefore \sin 2^{\circ }<\sin {65}^{\circ }$
$\Rightarrow x<y$