# Find the degree measures corresponding to the following radian measures:-$-4$ radians

$\begin{array}{1 1}(A)\;229^{\large\circ}&(B)\;230^{\large\circ}\\(C)\;-229^{\large\circ}5'27''&(D)\;229^{\large\circ}27''5'\end{array}$

Toolbox:
• $\pi$ radians=$180^{\large\circ}$
• 1 radian =$(\large\frac{180}{\pi})$
• $1^{\large\circ}=60'$
• $1'=60''$
We have $\pi$ radians =$\large\frac{22}{7}$ radian=$180^{\large\circ}$
$-4$ radian=$(-4\times \large\frac{180}{\pi})$
$\Rightarrow -4\times \large\frac{180}{22/7}$
$\Rightarrow \large\frac{-4\times 180\times 7}{22}$
$\Rightarrow -(\large\frac{2520}{11})$
$\Rightarrow-229^{\large\circ}5'27''$
Hence (C) is the correct answer.
answered Apr 16, 2014