Maths
Trigonometry
Right-Angled Triangle
|
Trigonometrical Identities
Sine Law
|
Cosine Law
|
Tangent Law
Right-Angled Triangle
Right-angled triangle where a is the shortest side adjacent to angle θ,
b
is the side opposite θ and
c
is the longest side (the hypotenuse)
cos
θ
=
a
c
sin
θ
=
b
c
tan
θ
=
sin
θ
cos
θ
=
b
a
csc
θ
=
1
sin
θ
=
c
b
cot
θ
=
1
tan
θ
=
a
b
sec
θ
=
1
cos
θ
=
c
a
Trigonometrical Identities
sin
(
-
x
)
=
-
sin
x
cos
(
-
x
)
=
cos
x
cos
2
A
+
sin
2
A
=
1
tan
(
-
x
)
=
-
tan
x
cos
2
A
=
1
+
sin
2
A
csc
(
-
x
)
=
-
csc
x
sin
2
A
=
1
-
cos
2
A
sec
(
-
x
)
=
sec
x
sec
2
A
=
1
+
tan
2
A
cot
(
-
x
)
=
-
cot
x
csc
2
A
=
1
+
cot
2
A
cos
(
A
+
B
)
=
cos
A
cos
B
-
sin
A
sin
B
cos
2
A
=
cos
2
A
-
sin
2
A
=
1
-
2
sin
2
A
=
2
cos
2
A
-
1
cos
(
A
-
B
)
=
cos
A
cos
B
+
sin
A
sin
B
sin
(
A
+
B
)
=
sin
A
cos
B
+
cos
A
sin
B
sin
(
A
-
B
)
=
sin
A
cos
B
-
cos
A
sin
B
sin
2
A
=
2
sin
A
cos
A
tan
(
A
+
B
)
=
tan
A
+
tan
B
1
-
tan
A
tan
B
tan
2
A
=
2
tan
A
1
-
tan
2
A
tan
(
A
-
B
)
=
tan
A
-
tan
B
1
+
tan
A
tan
B
sin
(
A
+
2
π
)
=
sin
A
cos
(
A
+
2
π
)
=
cos
A
2
sin
A
cos
B
=
sin
(
A
+
B
)
+
sin
(
A
-
B
)
sin
(
A
+
π
)
=
-
sin
A
2
sin
A
cos
B
=
cos
(
A
-
B
)
-
cos
(
A
+
B
)
cos
(
A
+
π
)
=
-
cos
A
2
cos
A
cos
B
=
cos
(
A
+
B
)
+
cos
(
A
-
B
)
tan
(
A
+
π
)
=
tan
A
sin
A
+
sin
B
=
2
sin
(
A
+
B
2
)
cos
(
A
-
B
2
)
sin
(
π
2
-
A
)
=
cos
A
cos
A
+
cos
B
=
2
cos
(
A
+
B
2
)
cos
(
A
-
B
2
)
cos
(
π
2
-
A
)
=
cos
A
cos
A
-
cos
B
=
-
2
sin
(
A
+
B
2
)
sin
(
A
-
B
2
)
sin
(
π
-
A
)
=
sin
A
cos
(
π
-
A
)
=
-
cos
A
cos
θ
+
b
sin
θ
=
R
cos
(
θ
-
α
)
cos
θ
+
b
sin
θ
=
R
cos
(
θ
-
α
)
where
R
=
a
2
+
b
2
,
cos
α
=
b
R
and
α
=
a
R
cos
θ
+
b
sin
θ
=
R
sin
(
θ
+
α
)
where
R
=
a
2
+
b
2
,
cos
α
=
b
R
and
α
=
a
R
Sine Law
Triangle where side
a
is opposite angle
A
, side
b
is opposite angle
B
and side
c
is opposite angle
C
a
sin
A
=
b
sin
B
=
c
sin
C
=
2
R
Cosine Law
Triangle where side
a
is opposite angle
A
, side
b
is opposite angle
B
and side
c
is opposite angle
C
c
2
=
a
2
+
b
2
-
2
a
b
cos
C
b
2
=
a
2
+
c
2
-
2
a
c
cos
B
a
2
=
b
2
+
c
2
-
2
b
c
cos
A
Tangent Law
Triangle where side
a
is opposite angle
A
, side
b
is opposite angle
B
and side
c
is opposite angle
C
a
-
b
a
+
b
=
tan
(
A
-
B
2
)
tan
(
A
+
B
2
)
[
H O M E
] [
S C I E N C E
] [
M A T H S
] [
A S T R O N O M Y
]
Download
|
Contact
|
About
Developed By
DOMEX E-DATA PVT., LTD.,
