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Question: Express the given angle in the degree, minutes, and seconds units, \(\dfrac{4{{\pi }^{c}}}{3}\)....

Express the given angle in the degree, minutes, and seconds units, 4πc3\dfrac{4{{\pi }^{c}}}{3}.

Explanation

Solution

Hint: We know that 1∘{{1}^{{}^\circ }} is equal to 60 minutes and 1 minute has 60 seconds. We will use this relation of degrees, minute and second to solve this question. Also πc{{\pi }^{c}} is equal to 180∘{{180}^{{}^\circ }}.

Complete step-by-step answer:
It is given in the question that we have to express the angles into degrees, minutes and seconds. To express the angle into degree minutes and seconds we will use the relation between degree, minutes and seconds.
We know that 1∘{{1}^{{}^\circ }} is equal to 60 minutes and 1 minute is equal to 60 seconds. Therefore, we can say that
1∘=60 minutes=60×60 seconds{{1}^{{}^\circ }}=60\text{ minutes}=60\times 60\text{ seconds}.
Now, we have to express 4πc3\dfrac{4{{\pi }^{c}}}{3} into degrees, minutes and seconds. We know that πc{{\pi }^{c}} means 180∘{{180}^{{}^\circ }}, therefore, 4πc3\dfrac{4{{\pi }^{c}}}{3}will be equal to 4×1803=4×60∘=240∘\dfrac{4\times 180}{3}=4\times {{60}^{{}^\circ }}={{240}^{{}^\circ }}
Calculation of minutes in 60 degrees is given by the following general formula=integer(decimal degrees − integer degrees)=integer\left( decimal\text{ }degrees\text{ }-\text{ }integer\text{ }degrees \right),
= int⁡(240∘−240∘)×60\operatorname{int}\left( {{240}^{{}^\circ }}-{{240}^{{}^\circ }} \right)\times 60,
=0′=0' .
Calculation of seconds can be done by using the following general formula =(decimal degrees − integer degrees−minutes60)×3600=\left( decimal\text{ }degrees\text{ }-\text{ }integer\text{ }degrees-\dfrac{\text{minutes}}{60} \right)\times 3600
=(240−240−060)×3600=\left( 240-240-\dfrac{0}{60} \right)\times 3600
=0′′=0''.
Thus, 4πc3\dfrac{4{{\pi }^{c}}}{3} is equal to 240∘0′0′′{{240}^{{}^\circ }}0'0''.

Note: Student may confuse that we do not have any value in decimal so how to convert this into minutes and seconds but it is very easy question and we can represent 60∘{{60}^{{}^\circ }} as 60∘0′0′′{{60}^{{}^\circ }}0'0''. It is essential to know these conversions so as to be very specific about the angle measurements. These units are less popular but we need to remember these conversions as they may be asked in the examinations easily and have less time consuming calculations as well.