MCQ
Which of the following is correct?
- A$\sin1^\circ>\sin1$
- ✓$\sin1^\circ<\sin1$
- C$\sin1^\circ=\sin1$
- D$\sin1^\circ=\frac{\pi}{180}\sin1$
✓
Answer
Correct option: B.
$\sin1^\circ<\sin1$
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 $1^\circ< 1$ radian
$\therefore\sin 1^\circ < \sin1$
Hence, the correct answer is option $B.$
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 $1^\circ< 1$ radian
$\therefore\sin 1^\circ < \sin1$
Hence, the correct answer is option $B.$
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