Question:
Which of the following is correct?
(a) $\sin 1^{\circ}>\sin 1$
(b) $\sin 1^{\circ}<\sin 1$
(c) $\sin 1^{\circ}=\sin 1$
(d) $\sin 1^{\circ}=\frac{\pi}{180} \sin 1$
Solution:
We know that, 1 radian is approximately 57º.
Also, the value of $\sin x$ is always increasing for $0 \leq x \leq 90^{\circ}$ ( or $\sin x$ is an increasing function for $0 \leq x \leq 90^{\circ}$ ).
NOW,
$1^{\circ}<57^{\circ}$
Or $1^{\circ}<1 \operatorname{radian}$
$\therefore \sin 1^{\circ}<\sin 1$
Hence, the correct answer is option B.