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 $1^{\prime} = 60^{\prime \prime}$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(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 $1^{\prime \prime} = \frac{2.908 \times 10^{-4}}{60} \text{ rad} \approx 4.847 \times 10^{-6} \text{ rad} \approx 4.85 \times 10^{-6} \text{ rad}$.

Explore More

Similar Questions

The difference between the length of a mean solar day and a sidereal day is approximately .......... minutes.

$(a)$ The earth-moon distance is about $60$ earth radii. What will be the angular diameter of the earth (approximately in degrees) as seen from the moon?
$(b)$ The moon is seen to have an angular diameter of $(1/2)^{\circ}$ from the earth. What is its relative size compared to the earth?
$(c)$ From parallax measurement,the sun is found to be at a distance of about $400$ times the earth-moon distance. Estimate the ratio of sun-earth diameters.

Write the ratio of the maximum and minimum time observed in the universe.

Why is the parallax method not used to measure the distance of stars that are $100$ light-years away?

Which of the following time measuring devices is most precise?
$(A)$ $A$ wall clock
$(B)$ $A$ stop watch
$(C)$ $A$ digital watch
$(D)$ An atomic clock
Give reason for your answer.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo