Which of the following is correct?(a) sin 1° > sin 1(b) sin 1° < sin 1(c) sin 1° = sin 1(d) sin 1° = π/180 sin 1

Question

\[ \text{Which of the following is correct?} \]

(a) \(\sin1^\circ>\sin1\)
(b) \(\sin1^\circ<\sin1\)
(c) \(\sin1^\circ=\sin1\)
(d) \(\sin1^\circ=\frac{\pi}{180}\sin1\)

Here,

\[ 1^\circ=\frac{\pi}{180}\text{ rad} \]

\[ \frac{\pi}{180}\approx0.017 \]

while

\[ 1\text{ rad}\approx57.3^\circ \]

Now,

\[ \sin1^\circ=\sin\left(\frac{\pi}{180}\right)\approx0.017 \]

\[ \sin1\approx0.84 \]

Therefore,

\[ \sin1^\circ<\sin1 \]

\[ \boxed{\sin1^\circ<\sin1} \]

Correct Option: (b)

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