50037′30′′=500+(376030)′=500+(275)′=500+(2×6075)0=(5085)0=(8405)01800=πc⇒10=(180π)c⇒(8405)0=(180π×8405)c=(329π)c

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50^037'30'' = ?

Question

$5 0^{0} 3 7^{'} 3 0^{''} = ?$

(\frac{5 π}{16})^{c}

(\frac{7 π}{18})^{c}

(\frac{9 π}{32})^{c}

(\frac{11 π}{36})^{c}

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Text solutionVerified

5 0^{0} 3 7^{'} 3 0^{''} = 5 0^{0} + (37 \frac{30}{60})^{'} = 5 0^{0} + (\frac{75}{2})^{'} = 5 0^{0} + (\frac{75}{2 \times 60})^{0} = (50 \frac{5}{8})^{0} = (\frac{405}{8})^{0}

18 0^{0} = π^{c} \Rightarrow 1^{0} = (\frac{π}{180})^{c} \Rightarrow (\frac{405}{8})^{0} = (\frac{π}{180} \times \frac{405}{8})^{c} = (\frac{9 π}{32})^{c}

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