Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

(a) $32.34^\circ$ (b) $63^\circ+10'+48''$
(a) We know the conversions $1^\circ=60'$ and $1'=60''$ Therefore, $32^\circ 20'35''=(32^\circ+\dfrac{20}{60}^\circ+\dfrac{35}{60\cdot60}^\circ) \approx 32.34^\circ$ (b) We know the conversions $1^\circ=60'$ and $1'=60''$ Therefore, $63.18^\circ=63^\circ+(0.18) \cdot (60') \\=63^\circ+10.8'\\=63^\circ+10'+(0.8) \cdot (60'') \\=63^\circ+10'+48''$