Question

If $\mathrm{\pi }=\frac{22}{7}$, then a unit radian is approximately equal to

• A. $57°{16}^{\text{'}}{22}^{\text{'}\text{'}}$
• B. $57°{15}^{\text{'}}{22}^{\text{'}\text{'}}$
• C. $57°{16}^{\text{'}}{20}^{\text{'}\text{'}}$
• D. $57°{15}^{\text{'}}{20}^{\text{'}\text{'}}$

Answer 1

The correct option is A

$57°{16}^{\text{'}}{22}^{\text{'}\text{'}}$

Explanation of the correct option:

Find the value of $1\mathrm{radian}$:

$\mathrm{\pi }\mathrm{radian}=180°$

$\begin{array}{rcl}& \Rightarrow & 1\mathrm{radian}=\frac{180°}{\mathrm{\pi }}\\ & =& \frac{180°}{{\displaystyle \frac{22}{7}}}[\because \mathrm{\pi }=\frac{22}{7}]\\ & =& \frac{180°\times 7}{22}\\ & =& \frac{630°}{11}\\ & =& {\left(57\frac{3}{11}\right)}^{°}\\ & =& 57°+{\left(\frac{3}{11}\right)}^{°}\\ & =& 57°+\frac{3}{11}\times 60\min [\because 1°=60\text{'}\min ]\\ & =& 57°+\frac{180}{11}\min \\ & =& 57°+16\frac{4}{11}\min \\ & =& 57°+16\text{'}+\frac{4}{11}\times 60\mathrm{s}[\because 1\text{'}\min =60\text{'}\text{'}\mathrm{s}]\\ & =& 57°+16\text{'}+21.8\text{'}\text{'}\\ & =& 57°16\text{'}22\text{'}\text{'}\left(\mathrm{approximately}\right)\end{array}$

Hence, the correct option is A.