Question

Determine os valores de:
a) Sec 120°
b) Cossec pi /3
c) Cotg 240°
d)tg 150°
e) Cotg 2 pi/ 3

Answer 1

a) $sec 120=\frac{1}{cos 120}=\frac{1}{-cos60}=\frac{1}{-\frac{1}{2}}=-2$

b) $csc(\pi/3)=\frac{1}{sen(\pi/3)}=\frac{1}{\frac{\sqrt{3}}{2}}=\frac{2\sqrt{3}}{3}$

c) $cot(240)=\frac{cos(240)}{sen(240)}=\frac{-cos(60)}{-sen(60)}=\frac{-1/2}{-\sqrt{3}/2}=\frac{\sqrt{3}}{3}$

d) $tan(150)=-tan(30)=-\frac{sen(30)}{cos(30)}=-\frac{1/2}{\sqrt{3}/2}=-\frac{\sqrt{3}}{3}$

e) $cot(2\pi/3)=-cot(\pi/3)=-\frac{cos(\pi/3)}{sen(\pi/3)}=-\frac{1/2}{\sqrt{3}/2}=-\frac{\sqrt{3}}{3}$