Trigonometric Functions — MATHS STD 11 Science — Question

2. $\sin1^\circ<\sin1$

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.