Calculate the angle of $(a)$ $1^{\circ}$ (degree),$(b)$ $1^{\prime}$ (minute of arc),and $(c)$ $1^{\prime \prime}$ (second of arc) in radians. Use $360^{\circ} = 2\pi \text{ rad}$,$1^{\circ} = 60^{\prime}$,and $1^{\prime} = 60^{\prime \prime}$.

(N/A) Since $360^{\circ} = 2\pi \text{ rad}$,we have $1^{\circ} = \frac{2\pi}{360} \text{ rad} = \frac{\pi}{180} \text{ rad} \approx 1.745 \times 10^{-2} \text{ rad}$.
$(b)$ Since $1^{\circ} = 60^{\prime} = 1.745 \times 10^{-2} \text{ rad}$,then $1^{\prime} = \frac{1.745 \times 10^{-2}}{60} \text{ rad} \approx 2.908 \times 10^{-4} \text{ rad} \approx 2.91 \times 10^{-4} \text{ rad}$.
$(c)$ Since $1^{\prime} = 60^{\prime \prime} = 2.908 \times 10^{-4} \text{ rad}$,then $1^{\prime \prime} = \frac{2.908 \times 10^{-4}}{60} \text{ rad} \approx 4.847 \times 10^{-6} \text{ rad} \approx 4.85 \times 10^{-6} \text{ rad}$.