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Kalkulus/Tabel trigonometri
Bahasa
Pantau
Sunting
<
Kalkulus
Daftar isi
1
Definisi
2
Identitas phytagoras
3
Identitas sudut ganda
4
Identitas sudut penjumlahan
5
Identitas perkalian menjadi penjumlahan
6
Lihat juga
Definisi
sunting
tan
(
x
)
=
sin
x
cos
x
{\displaystyle \tan(x)={\frac {\sin x}{\cos x}}}
sec
(
x
)
=
1
cos
x
{\displaystyle \sec(x)={\frac {1}{\cos x}}}
cot
(
x
)
=
cos
x
sin
x
=
1
tan
x
{\displaystyle \cot(x)={\frac {\cos x}{\sin x}}={\frac {1}{\tan x}}}
csc
(
x
)
=
1
sin
x
{\displaystyle \csc(x)={\frac {1}{\sin x}}}
Identitas phytagoras
sunting
sin
2
x
+
cos
2
x
=
1
{\displaystyle \sin ^{2}x+\cos ^{2}x=1\ }
1
+
tan
2
(
x
)
=
sec
2
x
{\displaystyle 1+\tan ^{2}(x)=\sec ^{2}x\ }
1
+
cot
2
(
x
)
=
csc
2
x
{\displaystyle 1+\cot ^{2}(x)=\csc ^{2}x\ }
Identitas sudut ganda
sunting
sin
(
2
x
)
=
2
sin
x
cos
x
{\displaystyle \sin(2x)=2\sin x\cos x\ }
cos
(
2
x
)
=
cos
2
x
−
sin
2
x
{\displaystyle \cos(2x)=\cos ^{2}x-\sin ^{2}x\ }
tan
(
2
x
)
=
2
tan
(
x
)
1
−
tan
2
(
x
)
{\displaystyle \tan(2x)={\frac {2\tan(x)}{1-\tan ^{2}(x)}}}
cos
2
(
x
)
=
1
+
cos
(
2
x
)
2
{\displaystyle \cos ^{2}(x)={1+\cos(2x) \over 2}}
sin
2
(
x
)
=
1
−
cos
(
2
x
)
2
{\displaystyle \sin ^{2}(x)={1-\cos(2x) \over 2}}
Identitas sudut penjumlahan
sunting
sin
(
x
+
y
)
=
sin
x
cos
y
+
cos
x
sin
y
{\displaystyle \sin \left(x+y\right)=\sin x\cos y+\cos x\sin y}
sin
(
x
−
y
)
=
sin
x
cos
y
−
cos
x
sin
y
{\displaystyle \sin \left(x-y\right)=\sin x\cos y-\cos x\sin y}
cos
(
x
+
y
)
=
cos
x
cos
y
−
sin
x
sin
y
{\displaystyle \cos \left(x+y\right)=\cos x\cos y-\sin x\sin y}
cos
(
x
−
y
)
=
cos
x
cos
y
+
sin
x
sin
y
{\displaystyle \cos \left(x-y\right)=\cos x\cos y+\sin x\sin y}
sin
x
+
sin
y
=
2
sin
(
x
+
y
2
)
cos
(
x
−
y
2
)
{\displaystyle \sin x+\sin y=2\sin \left({\frac {x+y}{2}}\right)\cos \left({\frac {x-y}{2}}\right)}
sin
x
−
sin
y
=
2
cos
(
x
+
y
2
)
sin
(
x
−
y
2
)
{\displaystyle \sin x-\sin y=2\cos \left({\frac {x+y}{2}}\right)\sin \left({\frac {x-y}{2}}\right)}
cos
x
+
cos
y
=
2
cos
(
x
+
y
2
)
cos
(
x
−
y
2
)
{\displaystyle \cos x+\cos y=2\cos \left({\frac {x+y}{2}}\right)\cos \left({\frac {x-y}{2}}\right)}
cos
x
−
cos
y
=
−
2
sin
(
x
+
y
2
)
sin
(
x
−
y
2
)
{\displaystyle \cos x-\cos y=-2\sin \left({\frac {x+y}{2}}\right)\sin \left({\frac {x-y}{2}}\right)}
tan
x
+
tan
y
=
sin
(
x
+
y
)
cos
x
cos
y
{\displaystyle \tan x+\tan y={\frac {\sin \left(x+y\right)}{\cos x\cos y}}}
tan
x
−
tan
y
=
sin
(
x
−
y
)
cos
x
cos
y
{\displaystyle \tan x-\tan y={\frac {\sin \left(x-y\right)}{\cos x\cos y}}}
cot
x
+
cot
y
=
sin
(
x
+
y
)
sin
x
sin
y
{\displaystyle \cot x+\cot y={\frac {\sin \left(x+y\right)}{\sin x\sin y}}}
cot
x
−
cot
y
=
−
sin
(
x
−
y
)
sin
x
sin
y
{\displaystyle \cot x-\cot y={\frac {-\sin \left(x-y\right)}{\sin x\sin y}}}
Identitas perkalian menjadi penjumlahan
sunting
cos
(
x
)
cos
(
y
)
=
cos
(
x
+
y
)
+
cos
(
x
−
y
)
2
{\displaystyle \cos \left(x\right)\cos \left(y\right)={\cos \left(x+y\right)+\cos \left(x-y\right) \over 2}\;}
sin
(
x
)
sin
(
y
)
=
cos
(
x
−
y
)
−
cos
(
x
+
y
)
2
{\displaystyle \sin \left(x\right)\sin \left(y\right)={\cos \left(x-y\right)-\cos \left(x+y\right) \over 2}\;}
sin
(
x
)
cos
(
y
)
=
sin
(
x
+
y
)
+
sin
(
x
−
y
)
2
{\displaystyle \sin \left(x\right)\cos \left(y\right)={\sin \left(x+y\right)+\sin \left(x-y\right) \over 2}\;}
cos
(
x
)
sin
(
y
)
=
sin
(
x
+
y
)
−
sin
(
x
−
y
)
2
{\displaystyle \cos \left(x\right)\sin \left(y\right)={\sin \left(x+y\right)-\sin \left(x-y\right) \over 2}\;}
Lihat juga
sunting
Trigonometri
