Question

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

Answer 1

Hint: We know that ${{1}^{{}^\circ }}$ 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 ${{\pi }^{c}}$ is equal to ${{180}^{{}^\circ }}$.

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 ${{1}^{{}^\circ }}$ is equal to 60 minutes and 1 minute is equal to 60 seconds. Therefore, we can say that
${{1}^{{}^\circ }}=60\text{ minutes}=60\times 60\text{ seconds}$.
Now, we have to express $\dfrac{4{{\pi }^{c}}}{3}$ into degrees, minutes and seconds. We know that ${{\pi }^{c}}$ means ${{180}^{{}^\circ }}$, therefore, $\dfrac{4{{\pi }^{c}}}{3}$will be equal to $\dfrac{4\times 180}{3}=4\times {{60}^{{}^\circ }}={{240}^{{}^\circ }}$
Calculation of minutes in 60 degrees is given by the following general formula$=integer\left( decimal\text{ }degrees\text{ }-\text{ }integer\text{ }degrees \right)$,
 = $\operatorname{int}\left( {{240}^{{}^\circ }}-{{240}^{{}^\circ }} \right)\times 60$,
$=0'$ .
Calculation of seconds can be done by using the following general formula $=\left( decimal\text{ }degrees\text{ }-\text{ }integer\text{ }degrees-\dfrac{\text{minutes}}{60} \right)\times 3600$
$=\left( 240-240-\dfrac{0}{60} \right)\times 3600$
$=0''$.
Thus, $\dfrac{4{{\pi }^{c}}}{3}$ is equal to ${{240}^{{}^\circ }}0'0''$.

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 ${{60}^{{}^\circ }}$ as ${{60}^{{}^\circ }}0'0''$. 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.