Question

Express the following angles in degrees.

(1) ${\left(\frac{5\pi }{12}\right)}^{\circ }$

(2) $-{\left(\frac{7\pi }{12}\right)}^{\circ }$

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

(4) $\frac{5{\pi }^{\circ }}{6}$

(5) $\frac{2{\pi }^{\circ }}{9}$

(6) $\frac{7{\pi }^{\circ }}{24}$

Answer 1

(1) $\frac{5\pi }{12}\equiv {(\frac{5\pi }{12}\times \frac{180}{\pi })}^0={75}^0$

(2) $-\left(\frac{7\pi }{12}\right)\equiv {360}^0-{(\frac{7\pi }{12}\times \frac{180}{\pi })}^0={360}^0-{105}^0={255}^0$

(3) $\frac{\pi }{3}\equiv {(\frac{\pi }{3}\times \frac{180}{\pi })}^0={60}^0$

(4) $\frac{5\pi }{6}\equiv {(\frac{5\pi }{6}\times \frac{180}{\pi })}^0={150}^0$

(5) $\frac{2\pi }{9}\equiv {(\frac{2\pi }{9}\times \frac{180}{\pi })}^0={40}^0$

(6) $\frac{7\pi }{24}\equiv (\frac{7\pi }{24}\times \frac{{180}^0}{\pi })={52.5}^0$