Aspire Faculty ID #3654 · Topic: NIMCET 2012 · Just now
NIMCET 2012

Which of the following is correct?

Solution

Here, $\sin 1^\circ$ means the angle is measured in degrees, while $\sin 1$ means the angle is measured in radians. Convert $1$ radian into degrees: $1\text{ radian}=\frac{180^\circ}{\pi}\approx57.3^\circ$ 

Therefore, $1^\circ<1\text{ radian}<90^\circ$ 
Since the sine function is increasing in the first quadrant, $\sin 1^\circ<\sin 1$ 

Therefore, the correct answer is: $\sin 1^\circ<\sin 1$
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