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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