Download Trigonometry Identities and Formula Sheet

MHF 4U1 – Grade 12 Advanced Functions
Unit 5: Trigonometric Functions, Part II
Trigonometric Identities and Formulas
Pythagorean Identity
Quotient Identity
Reciprocal Identities
sin 2 x  cos 2 x  1
sin x
 tan x
cos x
Alternate Forms:
Alternate Forms:
sin 2 x  1  cos 2 x
sin 2 x
 tan 2 x
2
cos x
1
sin x
1
sec x 
cos x
1
cot x 
tan x
cos 2 x  1  sin 2 x

New identities:


cos x  sin  x  
2



sin x  cos x   .
2

sin( b)   sin b
cos( b)  cos b

Addition and Subtraction Formulas:
sin( a  b)  sin a cos b  cos a sin b
sin( a  b)  sin a cos b  cos a sin b
cos( a  b)  cos a cos b  sin a sin b
cos( a  b)  cos a cos b  sin a sin b
tan a  tan b
, tan a tan b  1
1  tan a tan b
tan a  tan b
tan( a  b) 
, tan a tan b  1
1  tan a tan b
tan( a  b) 

Double Angle Formulas:
sin 2a  2 sin a cos a
cos 2a  cos 2 a  sin 2 a
cos 2a  2 cos 2 a  1
cos 2a  1  2 sin 2 a
2 tan a
tan 2a 
, tan a  1
1  tan 2 a
csc x 