ALL TRIG IDENTITIES & FORMULAS

Reciprocal:

sin x

1 / csc x

Reciprocal:

cos x

1 / sec x

Reciprocal:

tan x

1 / cot x

Reciprocal:

csc x

1 / sin x

Reciprocal:

sec x

1 / cos x

Reciprocal:

cot x

1 / tan x

Quotient:

tan x

sin x / cos x

Quotient:

cot x

cos x / sin x

Pythagorean:

1

sin^2 x + cos^2 x

Pythagorean:

sec^2 x

1 + tan^2 x

Pythagorean:

csc^2 x

1 + cot^2 x

Cofunction:

sin x

cos(90 - x)

Cofunction:

cos x

sin(90 - x)

Cofunction:

csc x

sec(90 - x)

Cofunction:

sec x

csc(90 - x)

Cofunction:

tan x

cot(90 - x)

Cofunction:

cot x

tan(90 - x)

Even/odd:

sin(-x)

-sin x

(odd)

Even/odd:

csc(-x)

-csc x

(odd)

Even/odd:

cos(-x)

cos x

(even)

Even/odd:

sec(-x)

sec x

(even)

Even/odd:

tan(-x)

-tan x

(odd)

Even/odd:

cot

-cot x

(odd)

Sum/difference:

sin(u + v)

sin u cos v +

cos u sin v

Sum/difference:

sin(u - v)

sin u cos v -

cos u sin v

Sum/difference:

cos(u + v)

cos u cos v -

sin u sin v

Sum/difference:

cos(u - v)

cos u cos v +

sin u sin v

Sum/difference:

tan(u + v)

tan u + tan v

--------------

1 - tan u tan v

Sum/difference:

tan (u - v)

tan u - tan v

--------------

1 + tan u tan v

Double angle:

sin 2u

2 sin u cos u

Double angle:

cos 2 u

(in terms of sine & cosine)

cos^2 u - sin^2 u

Double angle:

cos 2u

(in terms of sine)

1 - 2 sin^2 u

Double angle:

cos 2u

(in terms of cosine)

2 cos^2 u - 1

Double angle:

tan 2u

2 tan u

---------

1 - tan^2 u

Power reducing:

sin^2 u

1 - cos 2u

----------

2

Power reducing:

cos^2 u

cos 2u + 1

-----------

2

Power reducing:

tan^2 u

1 - cos 2u

----------

cos 2u + 1

Half angle:

sin u/2

+/- sqrt:

1 - cos u

---------

2

Half angle:

cos u/2

+/- sqrt:

1 + cos u

---------

2

Half angle:

tan u/2

(2 formulas)

1 - cos u

---------

sin u

OR

sin u

--------

1 + cos u

Law of Sines

a b c

----- = ------ = ------

sin A sin B sin C

Law of Cosines

a^2 = b^2 + c^2 - 2bc * cos A

Length of vector:

||v||

sqrt:

x^2 + y^2

(must be in component form)

Trig form of vector

||v||[(cos A)i + (sin A)j]