Statement Convert from degrees to radians, or from radians to degrees: (a) 23∘23^\circ23∘ (b) −143∘-143^\circ−143∘ (c) 34 rad34\ \text{rad}34 rad (d) 4 rad4\ \text{rad}4 rad Solution Use αrad=π180 αdeg\alpha_{\text{rad}}=\dfrac{\pi}{180}\,\alpha_{\text{deg}}αrad=180παdeg and αdeg=180π αrad\alpha_{\text{deg}}=\dfrac{180}{\pi}\,\alpha_{\text{rad}}αdeg=π180αrad. (a) 23∘=23π180≈0.4014 rad23^\circ=\dfrac{23\pi}{180}\approx0{.}4014\ \text{rad}23∘=18023π≈0.4014 rad. (b) −143∘=−143π180≈−2.4958 rad-143^\circ=-\dfrac{143\pi}{180}\approx-2{.}4958\ \text{rad}−143∘=−180143π≈−2.4958 rad. (c) 34 rad=34⋅180π≈1947.75∘34\ \text{rad}=34\cdot\dfrac{180}{\pi}\approx1947{.}75^\circ34 rad=34⋅π180≈1947.75∘ (which, reduced, equals ≈147.75∘\approx147{.}75^\circ≈147.75∘). (d) 4 rad=4⋅180π≈229.18∘4\ \text{rad}=4\cdot\dfrac{180}{\pi}\approx229{.}18^\circ4 rad=4⋅π180≈229.18∘. 0.4014 rad; −2.4958 rad; 1947.75∘; 229.18∘\boxed{0{.}4014\ \text{rad};\ -2{.}4958\ \text{rad};\ 1947{.}75^\circ;\ 229{.}18^\circ}0.4014 rad; −2.4958 rad; 1947.75∘; 229.18∘