Si la cotg Alfa = 2 y Alfa pertenece al tercer cuadrante, entonces el seno y el coseno son:
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Cuadrante III
sen < 0
cos < 0
tan > 0
cot > 0
sec < 0
csc < 0
cot(a) = 2
cos(a)/sen(a) = 2
cos^2(a)/sen^2(a) = 4
(cos^2(a)/sen^2(a)) + 1 = 4 + 1
(cos^2(a) + sen^2(a))/sen^2(a) = 5
csc^2(a) = 1/sen^2(a) = 5
csc(a) = -√5
sen(a) = -1/√5 = -(1/5) √5
cos(a) = sen(a) * cot(a) = -(2/√5) = -(2/5) √5
sec(a) = 1/cos(a) = -√5/2
tan(a) = 1/cot(a) = 1/2
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Hola
Cuadrante III
sen < 0
cos < 0
tan > 0
cot > 0
sec < 0
csc < 0
cot(a) = 2
cos(a)/sen(a) = 2
cos^2(a)/sen^2(a) = 4
(cos^2(a)/sen^2(a)) + 1 = 4 + 1
(cos^2(a) + sen^2(a))/sen^2(a) = 5
csc^2(a) = 1/sen^2(a) = 5
csc(a) = -√5
sen(a) = -1/√5 = -(1/5) √5
cos(a) = sen(a) * cot(a) = -(2/√5) = -(2/5) √5
sec(a) = 1/cos(a) = -√5/2
tan(a) = 1/cot(a) = 1/2