# Which of the following is correct?

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.