Which of the following is correct? - Vidyadip

MCQ

Which of the following is correct?

A
$\sin1^\circ>\sin1$
B
$\sin1^\circ<\sin1$
C
$\sin1^\circ=\sin1$
D
$\sin1^\circ=\frac{\pi}{180}\sin1$

✓

Answer

$\sin1^\circ<\sin1$

Solution:

We know that, 1 radian is approximately $57^\circ$.

Also, the value of $\sin\text{x}$ is always increasing for $0\leq \text{x}\leq 90^\circ$

$($or $\sin\text{x}$ is an increasing function for $0\leq \text{x}\leq 90^\circ).$

Now, $1^\circ < 57^\circ$

or $1^\circ< 1 \text{ radian}$

$\therefore\sin 1^\circ < \sin1$

Hence, the correct answer is option B.

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