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sen
θ
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s
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{\displaystyle \operatorname {sen} \theta ={\frac {\operatorname {a} }{c}}={\frac {\operatorname {cateto.opuesto} }{hipotenusa}}}
cos
θ
=
b
c
=
c
a
t
e
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o
.
a
d
y
a
c
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n
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h
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p
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s
a
{\displaystyle \cos \theta ={\frac {\operatorname {b} }{c}}={\frac {\operatorname {cateto.adyacente} }{hipotenusa}}}
tan
θ
=
a
b
=
c
a
t
e
t
o
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p
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s
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{\displaystyle \tan \theta ={\frac {\operatorname {a} }{b}}={\frac {\operatorname {cateto.opuesto} }{cateto.adyacente}}}
Relación inicial [ editar ]
tan
θ
=
sen
θ
cos
θ
{\displaystyle \tan \theta ={\frac {\operatorname {sen} \theta }{\cos \theta }}}
Teorema fundamental de la trigonometría [ editar ]
sen
2
θ
+
cos
2
θ
=
1
{\displaystyle \operatorname {sen} ^{2}\theta +\cos ^{2}\theta =1\,}
Equivalencia entre las funciones trigonométricas [ editar ]
Seno
Coseno
Tangente
Cotangente
Secante
Cosecante
s
e
n
θ
{\displaystyle sen\theta \,}
s
e
n
θ
{\displaystyle sen\theta \,}
1
−
c
o
s
2
θ
{\displaystyle {\sqrt {1-cos^{2}\theta }}}
t
a
n
θ
1
+
t
a
n
2
θ
{\displaystyle {\frac {tan\theta }{\sqrt {1+tan^{2}\theta }}}}
1
1
+
c
o
t
2
θ
{\displaystyle {\frac {1}{\sqrt {1+cot^{2}\theta }}}}
s
e
c
2
θ
−
1
s
e
c
θ
{\displaystyle {\frac {\sqrt {sec^{2}\theta -1}}{sec\theta }}}
1
c
s
c
θ
{\displaystyle {\frac {1}{csc\theta }}}
c
o
s
θ
{\displaystyle cos\theta \,}
1
−
s
e
n
2
θ
{\displaystyle {\sqrt {1-sen^{2}\theta }}}
c
o
s
θ
{\displaystyle cos\theta \,}
1
1
+
t
a
n
2
θ
{\displaystyle {\frac {1}{\sqrt {1+tan^{2}\theta }}}}
c
o
t
θ
1
+
c
o
t
2
θ
{\displaystyle {\frac {cot\theta }{\sqrt {1+cot^{2}\theta }}}}
1
s
e
c
θ
{\displaystyle {\frac {1}{sec\theta }}}
c
s
c
2
θ
−
1
c
s
c
θ
{\displaystyle {\frac {\sqrt {csc^{2}\theta -1}}{csc\theta }}}
t
a
n
θ
{\displaystyle tan\theta \,}
s
e
n
θ
1
−
s
e
n
2
θ
{\displaystyle {\frac {sen\theta }{\sqrt {1-sen^{2}\theta }}}}
1
−
c
o
s
2
θ
c
o
s
θ
{\displaystyle {\frac {\sqrt {1-cos^{2}\theta }}{cos\theta }}}
t
a
n
θ
{\displaystyle tan\theta \,}
1
c
o
t
θ
{\displaystyle {\frac {1}{cot\theta }}}
s
e
c
2
θ
−
1
{\displaystyle {\sqrt {sec^{2}\theta -1}}}
1
c
s
c
2
θ
−
1
{\displaystyle {\frac {1}{\sqrt {csc^{2}\theta -1}}}}
c
o
t
θ
{\displaystyle cot\theta \,}
1
−
s
e
n
2
θ
s
e
n
θ
{\displaystyle {\frac {\sqrt {1-sen^{2}\theta }}{sen\theta }}}
c
o
s
θ
1
−
c
o
s
2
θ
{\displaystyle {\frac {cos\theta }{\sqrt {1-cos^{2}\theta }}}}
1
t
a
n
θ
{\displaystyle {\frac {1}{tan\theta }}}
c
o
t
θ
{\displaystyle cot\theta \,}
1
s
e
c
2
θ
−
1
{\displaystyle {\frac {1}{\sqrt {sec^{2}\theta -1}}}}
c
s
c
2
θ
−
1
{\displaystyle {\sqrt {csc^{2}\theta -1}}}
s
e
c
θ
{\displaystyle sec\theta \,}
1
1
−
s
e
n
2
θ
{\displaystyle {\frac {1}{\sqrt {1-sen^{2}\theta }}}}
1
c
o
s
θ
{\displaystyle {\frac {1}{cos\theta \,}}}
1
+
t
a
n
2
θ
{\displaystyle {\sqrt {1+tan^{2}\theta }}}
1
+
c
o
t
2
θ
c
o
t
θ
{\displaystyle {\frac {\sqrt {1+cot^{2}\theta }}{cot\theta }}}
s
e
c
θ
{\displaystyle {sec\theta }\,}
c
s
c
θ
c
s
c
2
θ
−
1
{\displaystyle {\frac {csc\theta }{\sqrt {csc^{2}\theta -1}}}}
c
s
c
θ
{\displaystyle csc\theta \,}
1
s
e
n
θ
{\displaystyle {\frac {1}{sen\theta \,}}}
1
1
−
c
o
s
2
θ
{\displaystyle {\frac {1}{\sqrt {1-cos^{2}\theta }}}}
1
+
t
a
n
2
θ
t
a
n
θ
{\displaystyle {\frac {\sqrt {1+tan^{2}\theta }}{tan\theta }}}
1
+
c
o
t
2
θ
{\displaystyle {\sqrt {1+cot^{2}\theta }}}
s
e
c
θ
s
e
c
2
θ
−
1
{\displaystyle {\frac {sec\theta }{\sqrt {sec^{2}\theta -1}}}}
c
s
c
θ
{\displaystyle {csc\theta }\,}
sin(α+β)=sinα*cosβ+senβ*cosα
sin(α-β)=sinα*cosβ-sinβ*cosα
tan(α+Β)=(tanα+tanΒ) / (1-tanα*tanβ)
cos(α+β)=cosα*cosβ-sinα*sinβ
cos(α-β)cosα*cosβ+sinα*sinβ
sin(2α)=2*sinα*cosα
cos(2α)=cos^2(α)-sin^2(α)
tan(2α)=2*tan(α)/(1 - tan^2(α)) 
