Calculate the angle of $1^{\circ}$ (One degree) in radians.

Question

Accepted Answer

The correct option is (2):

To convert an angle from degrees to radians, we use the fundamental conversion factor which states that $180^\circ = \pi$ radians. This relationship is derived from the definition of a radian: an angle subtended at the center of a circle by an arc equal in length to the radius. A full circle is $360^\circ$ or $2\pi$ radians, so half a circle is $180^\circ$ or $\pi$ radians.

To find the value of $1^\circ$ in radians, we can set up a simple ratio or use the conversion formula:
Angle in radians = Angle in degrees $	imes \frac{\pi}{180^\circ}$

Substituting $1^\circ$ into the formula:
$1^\circ 	ext{ in radians} = 1 	imes \frac{\pi}{180} 	ext{ rad}$

Using the approximate value of $\pi \approx 3.14159$:
$1^\circ 	ext{ in radians} = \frac{3.14159}{180} 	ext{ rad}$
$1^\circ 	ext{ in radians} \approx 0.01745329 	ext{ rad}$

When rounded to three significant figures, this value is $1.745 	imes 10^{-2} 	ext{ rad}$. This matches option (2).

The incorrect option is (1): $2.3	imes10^{-2}rad$. This value is significantly different from the correct conversion and likely results from a computational error or an incorrect conversion factor.
The incorrect option is (3): $3.142	imes10^{-2}rad$. This value is close to $\frac{\pi}{100}$ (or $\pi 	imes 10^{-2}$), which indicates a misunderstanding of the divisor in the conversion formula.
The incorrect option is (4): $2.684	imes10^{-2}rad$. This value also deviates substantially from the accurate conversion, suggesting a calculation error during the conversion process.