Question

Calcule cotg x, sec x e cossec x para:
a) x= π/4
b) x = 150°

Answer 1

Resposta:

a) $x=\frac{\pi }{4} =45$

$cotg45=\frac{1}{tan45} =\frac{1}{1}=1$

$sec45=\frac{1}{cos45} =\frac{1}{\frac{\sqrt{2} }{2} } =\frac{2}{\sqrt{2} } =\frac{2\sqrt{2} }{2} =\sqrt{2}$

$cossec45=\frac{1}{sen45} =\frac{1}{\frac{\sqrt{2} }{2} } =\frac{2}{\sqrt{2} } =\frac{2\sqrt{2} }{2} =\sqrt{2}$

b)

$cotg150=\frac{1}{tan150} =\frac{1}{-\frac{\sqrt{3}}{3} }=-\frac{3}{\sqrt{3} } =-\frac{3\sqrt{3} }{3} =-\sqrt{3}$

$sec150=\frac{1}{cos150} =\frac{1}{-\frac{\sqrt{3} }{2} } =-\frac{2}{\sqrt{3} } =-\frac{2\sqrt{3} }{3}$

$cossec150=\frac{1}{sen150} =\frac{1}{\frac{1}{2} } =2$