Symbolab Trigonometry Cheat Sheet
[Pages:2]Symbolab Trigonometry Cheat Sheet
Basic Identities:
tan()
=
sin() cos()
tan()
=
1 cot()
cot()
=
1 tan()
cot()
=
cos() sin()
sec()
=
1 cos()
csc()
=
1 sin()
Pythagorean Identities cos2() + sin2() = 1 sec2() - tan2() = 1
csc2() - cot2() = 1
Double Angle Identities
sin(2) = 2 sin() cos() cos(2) = 1 - 2 sin2() cos(2) = 2 cos2() - 1
cos(2) = cos2() - sin2()
tan(2)
=
2 tan() 1-tan2()
Sum Difference Identities
sin( + ) = sin() cos() + cos() sin()
sin( - ) = sin() cos() - cos() sin()
cos( + ) = cos() cos() - sin() sin()
cos( - ) = cos() cos() + sin() sin()
tan(
+
)
=
tan()+tan() 1-tan() tan()
tan(
-
)
=
tan()-tan() 1+tan() tan()
Product To Sum Identities
cos() cos() = cos(-)+cos(+)
2
sin() sin() = cos(-)-cos(+)
2
Triple Angle Identities
sin(3) = - sin3() + 3 cos2() sin()
sin(3) = -4 sin3() + 3 sin()
cos(3) = cos3() - 3 sin2() cos()
cos(3) = 4 cos3() - 3 cos()
tan(3)
=
3
tan()-tan3() 1-3 tan2()
cot(3)
=
3 cot()-cot3() 1-3 cot2()
sin() cos() = sin(+)+sin(-)
2
cos() sin() = sin(+)-sin(-)
2
Function Ranges:
sin()
-1 1
cos() tan()
cot() csc()
sec()
-1 1 < <
< < - < 1 1 < - < 1 1 <
Function Values:
() 0 1
2
2
2 3
2 1
3
2 2
2 1
2
0 1 -2
-
2 2
-
3 2
-1
3 -2
-
2 2
1
-2
arcsin()
arccos() arctan()
arccot() arccsc()
arcsec()
() 1 3
2 2
2 1
2 0
1 -2
-
2 2
-
3 2
-1
3 -2
-
2 2
1
-2
0
1 2 2 2 3 2
- 2 2
0
- 2 < < 2
0 < <
3
0 < 2 < 2
- < - 2 0 < < 2
() 0
3
3 1
3
Undefined
-3
-
3 3
-1
0
() Undefined
3
1
3
3 0
-
3 3
-3
-1
Undefined
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