Trigonometric Identities

[godzilla2012]

You will encounter these in Pre-calculus and have to know these in Calculus.

BASIC IDENTITIES

• sin x = 1/csc x
• cos x = 1/sec x
• tan x = 1/cot x
• csc x = 1/sin x
• sec x = 1/cos x
• cot x = 1/tan x
• sin (-x) = -sin x
• cos(-x) = cos x
• tan (-x) = tan x
• tan x = sin x/cos x
• cot x = sin x/cos x

PYTHAGOREAN IDENTITIES

sin^2 (x) + cos^2 (x) = 1
1 + cot^2 (x) = csc^2 (x)
1 + tan^2 (x) = sec^2 (x)

SUM AND DIFFERENCE IDENTITIES

sin (u + v) = sin u cos v + cos u sin v
sin (u - v) = sin u cos v - cos u sin v
cos (u + v) = cos u cos v - sin u sin v
cos (u - v) = cos u cos v + sin u sin v
tan (u + v) = (tan u + tan v)/(1 - tan u tan v)
tan (u - v) = (tan u - tan v)/(1 + tan u tan v)

DOUBLE ANGLE IDENTITIES

sin2x = 2sinxcosx
cos2x = cos^2x - sin^2x
= 1 - 2sin^2x
= 2cos^2x - 1
tan2x = 2tanx/1 - tan^2x

HALF ANGLE IDENTITIES

sin x/2 = (+-)root[(1-cosx)/2]
cos x/2 = (+-)root[(1+cosx)/2]
tan x/2 = (+-)root[(1-cosx)/1+cosx)]
= sinx/1+cosx
= 1-cosx/sinx

Will add the rest later.

[Dr.Dental]

You usually have a formula sheet for all these... Make sure csc is cosec so ppl understand easier.