Question

01) Transforme em radianos:
a) 40°
b) 36°
c) 150°
d) 120°

02) Transforme em graus:
a) /6
b) / 8
c) 5/ 9
d) 3/ 40

Answer 1

Explicação passo-a-passo:

Para transformar em radianos basta multiplicar por $\pi$ e dividir por $180$

a) $40^{\circ}=\dfrac{40\pi}{180}\dfrac{\div20}{\div20}=\dfrac{2\pi}{9}~\text{rad}$

b) $36^{\circ}=\dfrac{36\pi}{180}\dfrac{\div36}{\div36}=\dfrac{\pi}{5}~\text{rad}$

c) $150^{\circ}=\dfrac{150\pi}{180}\dfrac{\div30}{\div30}=\dfrac{5\pi}{6}~\text{rad}$

d) $120^{\circ}=\dfrac{120\pi}{180}\dfrac{\div60}{\div60}=\dfrac{2\pi}{3}~\text{rad}$

Para transformar em graus basta multiplicar por 180° e dividir por $\pi$

a) $\dfrac{\pi}{6}~\text{rad}=\dfrac{180\pi}{6\pi}=30^{\circ}$

b) $\dfrac{\pi}{8}~\text{rad}=\dfrac{180\pi}{8\pi}=22,5^{\circ}$

c) $\dfrac{5\pi}{9}~\text{rad}=\dfrac{180\cdot5\pi}{9\pi}=100^{\circ}$

d) $\dfrac{3\pi}{40}~\text{rad}=\dfrac{180\cdot3\pi}{40\pi}=13,5^{\circ}$