Question

Convert 5pi/7 radians to degrees.

(Use pi = 3.14 when necessary and round your final answer to the hundredths place.)

5pi/7radians=________ degrees

Answer 1

well, since we know there are 180° in π/2 radians, then, what's 5π/7 radians?

`\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&(\pi )/(2)\\[1em] d&(5\pi )/(7) \end{array}\implies \cfrac{180}{d}~~ = ~~\cfrac{(\pi )/(2)}{ ~~ (5\pi )/(7) ~~ }\implies \cfrac{180}{d}=\cfrac{\pi }{2}\cdot \cfrac{7}{5\pi } \\\\\\ \cfrac{180}{d}=\cfrac{7}{10}\implies 1800=7d\implies \cfrac{1800}{7}=d\implies 257.14^o\approx d`