Question

Encontre a primeira determinação positiva dos arcos trigonométricos a seguir.
a) 1460°
b) 960°
c) -400°
d) -1180°
e) 11Pi/4 rad
f) 31Pi/2 rad​​

Answer 1

Explicação passo-a-passo:

a)

$\sf 1460^{\circ}=(1460^{\circ}-4\cdot360^{\circ})$

$\sf 1460^{\circ}=(1460^{\circ}-1440^{\circ})$

$\sf 1460^{\circ}=\red{20^{\circ}}$

b)

$\sf 920^{\circ}=(920^{\circ}-2\cdot360^{\circ})$

$\sf 920^{\circ}=(920^{\circ}-720^{\circ})$

$\sf 920^{\circ}=\red{200^{\circ}}$

c)

$\sf -400^{\circ}=(-400^{\circ}+2\cdot360^{\circ})$

$\sf -400^{\circ}=(-400^{\circ}+720^{\circ})$

$\sf -400^{\circ}=\red{320^{\circ}}$

d)

$\sf -1180^{\circ}=(-1180^{\circ}+4\cdot360^{\circ})$

$\sf -1180^{\circ}=(-1180^{\circ}+1440^{\circ})$

$\sf -1180^{\circ}=\red{260^{\circ}}$

e)

$\sf \dfrac{11\pi}{4}~rad=\Big(\dfrac{11\pi}{4}-2\pi\Big)$

$\sf \dfrac{11\pi}{4}~rad=\Big(\dfrac{11\pi-8\pi}{4}\Big)$

$\sf \dfrac{11\pi}{4}~rad=\red{\dfrac{3\pi}{4}~rad}$

f)

$\sf \dfrac{31\pi}{2}~rad=\Big(\dfrac{31\pi}{4}-7\cdot2\pi\Big)$

$\sf \dfrac{31\pi}{2}~rad=\Big(\dfrac{31\pi}{2}-14\pi\Big)$

$\sf \dfrac{31\pi}{2}~rad=\Big(\dfrac{31\pi-28\pi}{2}\Big)$

$\sf \dfrac{31\pi}{2}~rad=\red{\dfrac{3\pi}{2}~rad}$

Answer 2

a)20°

b)200°

c)320°

d)260°

$e) \frac{3\pi}{4} rad \\ \\ f) \frac{3\pi}{2} rad$