Question

Convert the following angle from degrees to radians. Express your answer in simplest form 345 ∘

Answer 1

well, since we know that there are 180° in π radians, how many degrees will it be in 345°?

$\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ 345&x \end{array}\implies \cfrac{180}{345}~~ = ~~\cfrac{\pi }{x}\implies \cfrac{12}{23}~~ = ~~\cfrac{\pi }{x} \\\\\\ 12x=23\pi \implies x=\cfrac{23\pi }{12}$