Question

11. Calcule os valores de:
a) sec pi/3

b) sec 135º

c) cossec 150°

d) cotg pi/4

e) cossec 240°

f) cotg 330°

me ajudem pfv eu não seiii​

Answer 1

Resposta:

a) 2 ; b) $-\sqrt{2}$ ; c) 2 ; d) 1 ; e) $-\frac{2\sqrt{3}}{3}$ ; f) $-\sqrt{3}$ .

Explicação passo-a-passo:

a) $sec (\pi /3)= \frac{1}{cos (\pi /3) } =\frac{1}{cos 60 } =\frac{1}{0,5} =2.$

b) $sec 135 = \frac{1}{cos135}=\frac{1}{-cos45} =-\frac{1}{\sqrt{2}/2 }=-\frac{2}{\sqrt{2} } =-\sqrt{2} .$

c) $cossec 150=\frac{1}{sen150} =\frac{1}{sen30} =\frac{1}{0,5} =2.$

d) $cotg(\pi/4) =\frac{1}{tg (\pi /4)}=\frac{1}{tg45} =\frac{1}{1} =1.$

e) $cossec 240 = \frac{1}{sen240}=\frac{1}{-sen60}=\frac{1}{-\sqrt{3}/2} =-\frac{2}{\sqrt{3}}=-\frac{2\sqrt{3}}{3}$

f) $cotg 330 = \frac{1}{tg330} =\frac{1}{-tg30}=\frac{1}{-\sqrt{3}/3 } =-\frac{3}{\sqrt{3}}=-\sqrt{3}$