Question

Express in degree, minutes, and seconds the angles $\dfrac{{{\pi }^{c}}}{3}$.

Answer 1

Hint: We know that ${{1}^{{}^\circ }}$ is equal to 60 minutes. Also 1 minute is equal to 60 seconds. We will use this relation to express $\dfrac{{{\pi }^{c}}}{3}$ into degrees, minutes and seconds. Also ${{\pi }^{c}}$ is equal to ${{180}^{{}^\circ }}$.

Complete step-by-step solution
It is given in the question that to express the angle $\dfrac{{{\pi }^{c}}}{3}$ 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 $\dfrac{{{\pi }^{c}}}{3}$ into degrees, minutes and seconds. We know that ${{\pi }^{c}}$ means ${{180}^{{}^\circ }}$, therefore, $\dfrac{{{\pi }^{c}}}{3}$will be equal to $\dfrac{180}{3}={{60}^{{}^\circ }}$
Calculation of minutes in 60 degrees is given by the following general formula$=integer\left( decimal\text{ }degrees\text{ }-\text{ }integer\text{ }degrees \right)$,
 = $\operatorname{int}\left( {{60}^{{}^\circ }}-{{60}^{{}^\circ }} \right)\times 60$,
$=0'$ .
Calculation of seconds can be done by using the following general formula $=\left( decimal\text{ }degrees\text{ }-\text{ }integer\text{ }degrees-\dfrac{\text{minutes}}{60} \right)\times 3600$
$=\left( 60-60-\dfrac{0}{60} \right)\times 3600$
$=0''$.
Thus, $\dfrac{{{\pi }^{c}}}{3}$ is equal to ${{60}^{{}^\circ }}0'0''$.

Note: Student may confuse that we do not have any value in decimal so how to convert this into minutes and seconds and they may leave this question in the examination, but it is a 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.