Question

Convert -3pi/10 to degrees

Answer 1

we know there are 180° in π radians, how many degrees then in -3π/10 radians?

`\bf \begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\\\ x&-(3\pi )/(10) \end{array}\implies \cfrac{180}{x}=\cfrac{\pi }{~~-(3\pi )/(10)~~}\implies \cfrac{180}{x}=\cfrac{(\pi)/(1) }{~~-(3\pi )/(10)~~} \\\\\\ \cfrac{180}{x}=\cfrac{\pi }{1}\cdot \cfrac{10}{-3\pi }\implies \cfrac{180}{x}=-\cfrac{10}{3}\implies 540=-10x\implies \cfrac{540}{-10}=x \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill -54=x~\hfill`