NIMCET 2012 — Mathematics PYQ

1. Understanding the Units:

• $1^{\circ }$ is measured in degrees.

• $1$ is measured in radians (since no unit is specified).

2. Conversion:

We know that $\pi$ radians $=180^{\circ }$.

Taking $\pi \approx 3.14$:

So, we are comparing $\sin 1^{\circ }$ and $\sin 57.3^{\circ }$.

3. Behavior of the Sine Function:

In the first quadrant ($0^{\circ }$ to $90^{\circ }$), the sine function is increasing. This means if \theta_1 < \theta_2, then \sin \theta_1 < \sin \theta_2.

Since:

It follows that:

Conclusion:

The value of $\sin 1$ is significantly larger than $\sin 1^{\circ }$.

Correct Option: (b)