Debo encontrar los valores exactos de senΘ, cosΘ, tanΘ, cotΘ, secΘ, cscΘ, si el lado terminal de Θ en posicion normal contiene el punto dado.
1. p(3,-4)
2. P(-5,-12)
3 P(-5,5)
Hola
1) P(3,-4)
3;-4 son los catetos
La hipotenusa es
raiz( (3)^2 + (-4)^2) = raiz(9+16) = raiz(25) = 5
senΘ = -4/5
cosΘ = 3/5
tanΘ = -4/3
cotΘ = 3/-4 = -3/4
secΘ = 5/3
cscΘ = 5/-4 = -5/4
1) P(-5,-12)
-5;-12 son los catetos
raiz( (-5)^2 + (-12)^2) = raiz(25+144) = raiz(169) = 13
senΘ = -12/13
cosΘ = -5/13
tanΘ = -12/-5 = 12/5
cotΘ = -5/-12 = 5/12
secΘ = 13/-5 = -13/5
cscΘ = 13/-12 = -13/12
3) P(-5,5)
-5;5 son los catetos
√( (-5)^2 + (5)^2) = √(25+25) = √(2*25) = 5 √(2)
senΘ = 5/(5 √(2)) = 1/√(2)
cosΘ = -5/(5 √(2)) = -1/√(2)
tanΘ = 5/-5 = -1
cotΘ = -5/5 = -1
secΘ = (5 √(2))/-5 = -√(2)
cscΘ = (5 √(2))/5 = √(2)
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Verified answer
Hola
1) P(3,-4)
3;-4 son los catetos
La hipotenusa es
raiz( (3)^2 + (-4)^2) = raiz(9+16) = raiz(25) = 5
senΘ = -4/5
cosΘ = 3/5
tanΘ = -4/3
cotΘ = 3/-4 = -3/4
secΘ = 5/3
cscΘ = 5/-4 = -5/4
1) P(-5,-12)
-5;-12 son los catetos
La hipotenusa es
raiz( (-5)^2 + (-12)^2) = raiz(25+144) = raiz(169) = 13
senΘ = -12/13
cosΘ = -5/13
tanΘ = -12/-5 = 12/5
cotΘ = -5/-12 = 5/12
secΘ = 13/-5 = -13/5
cscΘ = 13/-12 = -13/12
3) P(-5,5)
-5;5 son los catetos
La hipotenusa es
√( (-5)^2 + (5)^2) = √(25+25) = √(2*25) = 5 √(2)
senΘ = 5/(5 √(2)) = 1/√(2)
cosΘ = -5/(5 √(2)) = -1/√(2)
tanΘ = 5/-5 = -1
cotΘ = -5/5 = -1
secΘ = (5 √(2))/-5 = -√(2)
cscΘ = (5 √(2))/5 = √(2)