Question

43°40' = radians
(Round to the nearest thousandth.)

Answer 1

well, we know there are 60 minutes in 1 degree, so in 40 minutes that'll be 40/60 degrees or namely 2/3 of a degree.

We know that 180° is π radians, so let's find 43 ⅔ degrees

`\stackrel{mixed}{43(2)/(3)}\implies \cfrac{43\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{131}{3}} \\\\[-0.35em] ~\dotfill`

`\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\\\ (131)/(3)&x \end{array}\implies \cfrac{180}{~~ ( 131)/(3 ) ~~} = \cfrac{\pi }{x}\implies \cfrac{(180)/(1)}{~~ ( 131)/(3 ) ~~} = \cfrac{\pi }{x} \implies \cfrac{180}{1}\cdot \cfrac{3}{131}=\cfrac{\pi }{x} \\\\\\ \cfrac{540}{131}=\cfrac{\pi }{x}\implies 540x=131\pi \implies x=\cfrac{131\pi }{540}\implies x\approx 0.762~radians`