Question

escreva a primeira determinação positiva do arco de: 45pi/4 e 125pi/12

Answer 1

a)

$\frac{45\pi}{4} \times \frac{1}{2\pi} = \frac{45}{8 } \\ = \frac{40}{8} + \frac{5}{8} = 5 + \frac{5}{8}$

$\frac{45\pi}{4} = (5 + \frac{5}{8} )2\pi = \frac{5\pi}{4}$

b)

$\frac{125\pi}{12} \times \frac{1}{2\pi} = \frac{125}{24} \\ = \frac{120}{24} + \frac{5}{4} \\ 5 + \frac{5}{24}$

$\frac{125\pi}{12} = (5 + \frac{5}{24} ) \times 2\pi = \frac{5\pi}{12}$