Question

Calcule a cotg 4pi/3

Answer 1

Ola Lenilson

4π/3 ⇒ 4*180/3 = 240° = 180° + 60°

sen(240) = sen(180 + 60) = sen(180)*cos(60) + cos(180)*sen(60)
sen(240) = 0*1/2 -1*√3/2 = -√3/2

cos(240) = cos(180 + 60) = cos(180)*cos(60) - sen(180)*sen(60) 
cos(240) = -1*1/2 - 0*√3/2 = -1/2

cotg(240) = cos(240)/sen(240) = (-1/2)/(-√3/2) = 1/√3

cotg(240) = √3/3 

Answer 2

Vejamos:
180>>>> pi.rad
x>>>>>> 4pirad/3
x=240°
Cotg 240°=cos240/sen240
240°=180+60
cos240°=-cos60°
sen240=-sen60°
cos60°=1/2 e sen60°=V3/2
cotg240°=(-1/2)÷(-V3/2)=1/2×2/V3=1/V3=V3/(V3.V3)=
V3/3
cotg240°=cotg4pi/3=V3/3
Abraços.