Question

If $x=\sin 2^{\circ }$ and $y=\sin 2$ (where $2$ is in radian), 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 $x<y$

$1\text{radian}={\left(\frac{180}{\pi }\right)}^{\circ }\approx {57}^{\circ }{18}^{\prime }$
$2\text{radian}\approx {114}^{\circ }{36}^{\prime }$


From graph, $\sin 2>\sin 2^{\circ }$ i.e. $y>x$