# Find the degree measures corresponding to the following radian measures

Question:

Find the degree measures corresponding to the following radian measures

$\left(\right.$ Use $\left.\pi=\frac{22}{7}\right)$

(i) $\frac{11}{16}$

(ii) $-4$

(iii) $\frac{5 \pi}{3}$

(iv) $\frac{7 \pi}{6}$

Solution:

(i) $\frac{11}{16}$

We know that $\pi$ radian $=180^{\circ}$

$\therefore \frac{11}{16}$ radain $=\frac{180}{\pi} \times \frac{11}{16}$ deg ree $=\frac{45 \times 11}{\pi \times 4}$ deg ree

$=\frac{45 \times 11 \times 7}{22 \times 4}$ deg ree $=\frac{315}{8}$ deg ree

$=39 \frac{3}{8}$ deg ree

$=39^{\circ}+\frac{3 \times 60}{8}$ min utes $\quad\left[1^{\circ}=60^{\prime}\right]$

$=39^{\circ}+22^{\prime}+\frac{1}{2}$ min utes

$=39^{\circ} 22^{\prime} 30^{\prime \prime} \quad\left[1^{\prime}=60^{\prime \prime}\right]$

(ii) $-4$

We know that $\pi$ radian $=180^{\circ}$

$-4 \mathrm{radian}=\frac{180}{\pi} \times(-4)$ deg $\mathrm{ree}=\frac{180 \times 7(-4)}{22}$ deg ree

$=\frac{-2520}{11}$ deg ree $=-229 \frac{1}{11}$ deg ree

$=-229^{\circ}+\frac{1 \times 60}{11}$ min utes $\quad\left[1^{\circ}=60^{\prime}\right]$

$=-229^{\circ}+5^{\prime}+\frac{5}{11}$ min utes

$=-229^{\circ} 5^{\prime} 27^{\prime \prime} \quad\left[1^{\prime}=60^{\prime \prime}\right]$

(iii) $\frac{5 \pi}{3}$

We know that $\pi$ radian $=180^{\circ}$

$\therefore \frac{5 \pi}{3}$ radian $=\frac{180}{\pi} \times \frac{5 \pi}{3}$ deg ree $=300^{\circ}$

(iv) $\frac{7 \pi}{6}$

We know that $\pi$ radian $=180^{\circ}$

$\therefore \frac{7 \pi}{6} \operatorname{radian}=\frac{180}{\pi} \times \frac{7 \pi}{6}=210^{\circ}$