Question

expressar em rad 67°30

Answer 1

$\boxed{1^{\circ}=60'\;\;\Leftrightarrow\;\;1'=\dfrac{1}{60}^{\circ}}$


Então

$67^{\circ}30'\\ \\ =67^{\circ}+30'\\ \\ =67^{\circ}+30\cdot \dfrac{1}{60}^{\circ}\\ \\ =67^{\circ}+\dfrac{30}{60}^{\circ}\\ \\ =67^{\circ}+0,5^{\circ}\\ \\ =67,5^{\circ}$


$\boxed{1^{\circ}=\dfrac{\pi}{180}\text{ rad}\;\;\Leftrightarrow\;\;1 \text{ rad}=\dfrac{180^{\circ}}{\pi}}$


Então

$67^{\circ}30'\\ \\ =67,5^{\circ}\\ \\ =67,5\cdot \dfrac{\pi}{180}\text{ rad}\\ \\ =\dfrac{67,5\pi}{180} \text{ rad}\\ \\ =\dfrac{67,5\pi \cdot 2}{180 \cdot 2} \text{ rad}\\ \\ =\dfrac{135\pi}{360} \text{ rad}\\ \\ =\dfrac{135\pi \div 45}{360 \div 45} \text{ rad}\\ \\ =\dfrac{3\pi}{8} \text{ rad}\\ \\ \\ \boxed{67^{\circ}30'=\dfrac{3\pi}{8} \text{ rad}}$