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Trigonometry Formulas
Step-by-Step Examples
Unit Circle
Unit Circle Values
Reciprocal Identities
sin
θ
=
1
csc
θ
cos
θ
=
1
sec
θ
tan
θ
=
1
cot
θ
cot
θ
=
1
tan
θ
sec
θ
=
1
cos
θ
csc
θ
=
1
sin
θ
sin
θ
=
1
csc
θ
cos
θ
=
1
sec
θ
tan
θ
=
1
cot
θ
cot
θ
=
1
tan
θ
sec
θ
=
1
cos
θ
csc
θ
=
1
sin
θ
Ratio Indentities
tan
θ
=
sin
θ
cos
θ
cot
θ
=
cos
θ
sin
θ
tan
θ
=
sin
θ
cos
θ
cot
θ
=
cos
θ
sin
θ
Pythagorean Identities
sin
2
θ
+
cos
2
θ
=
1
1
+
tan
2
θ
=
sec
2
θ
1
+
cot
2
θ
=
csc
2
θ
sin
2
θ
+
cos
2
θ
=
1
1
+
tan
2
θ
=
sec
2
θ
1
+
cot
2
θ
=
csc
2
θ
Sum and Difference Formulas
sin
(
A
+
B
)
=
sin
A
cos
B
+
cos
A
sin
B
sin
(
A
−
B
)
=
sin
A
cos
B
−
cos
A
sin
B
cos
(
A
+
B
)
=
cos
A
cos
B
−
sin
A
sin
B
cos
(
A
−
B
)
=
cos
A
cos
B
+
sin
A
sin
B
tan
(
A
+
B
)
=
tan
A
+
tan
B
1
−
tan
A
tan
B
tan
(
A
−
B
)
=
tan
A
−
tan
B
1
+
tan
A
tan
B
sin
(
A
+
B
)
=
sin
A
cos
B
+
cos
A
sin
B
sin
(
A
-
B
)
=
sin
A
cos
B
-
cos
A
sin
B
cos
(
A
+
B
)
=
cos
A
cos
B
-
sin
A
sin
B
cos
(
A
-
B
)
=
cos
A
cos
B
+
sin
A
sin
B
tan
(
A
+
B
)
=
tan
A
+
tan
B
1
-
tan
A
tan
B
tan
(
A
-
B
)
=
tan
A
-
tan
B
1
+
tan
A
tan
B
Double-Angle Formulas
sin
2
A
=
2
sin
A
cos
A
cos
2
A
=
cos
2
A
−
sin
2
A
=
2
cos
2
A
−
1
=
1
−
2
sin
2
A
tan
2
A
=
2
tan
A
1
−
tan
2
A
sin
2
A
=
2
sin
A
cos
A
cos
2
A
=
cos
2
A
-
sin
2
A
=
2
cos
2
A
-
1
=
1
-
2
sin
2
A
tan
2
A
=
2
tan
A
1
-
tan
2
A
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