Download Trigonometry Identities Math 170 “Pre

Trigonometry Identities
Math 170 “Pre-Calculus”
*Reciprocal Identities:
1
csc x
1
cos x =
sec x
1
tan x =
cot x
sin x =
1
tan x
1
sec x =
cos x
1
csc x =
sin x
cot x =
*Pythagorean Identities:
*Quotient Identities:
sin x
cosx
cos x
cot x =
sin x
tan x =
Double Angle Identities:
* sin2x = 2sin x cos x
cos2 x + sin 2 x = 1
* cos2x = cos2 x − sin2 x
tan2 x + 1 = sec 2 x
* cos2x = 2cos2 x − 1
cot 2 x + 1= csc 2 x
* cos2x = 1− 2sin2 x
2tan x
tan 2x =
1− tan2 x
Half-Angle Identities:
Sum and Difference Identities:
1
1− cos x
sin( x) = ±
2
2
sin(x + y) = sin x cos y + cosx sin y
sin(x − y) = sin x cos y − cosx sin y
cos(x + y) = cos x cos y − sin x sin y
1
1 + cos x
cos( x) = ±
2
2
1
1− cos x
tan( x) = ±
2
1 + cosx
Even/Odd Identities:
Identities:
sin(−u) = − sin u
cos(−u) = cos u
tan(−u) = − tan u
cos(x − y) = cos x cosy + sin x sin y
tan x + tan y
1− tan x tan y
tan x − tan y
tan( x − y) =
1+ tan x tan y
tan( x + y) =
Cofunction
π
sin( − u) = cosu
2
π
tan( − u) = cot u
2
π
cos( − u) = sinu
2
* Must have these memorized for Test and Final Exam*