Trigonometric Formula Sheet
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1
2Trigonometric Identities
Reciprocal Identities
Complement Formulas
1
1
sinx = cos (90–x)
sin x =
csc x =
csc x
sin x
cosx = sin (90–x)
1
1
cos x =
sec x =
tanx = cot (90–x)
sec x
cosx
cotx = tan (90–x)
1
sin x
tan x =
tan x =
cot x
cosx
secx = csc (90–x)
1
cosx
cot x =
cot x =
cscx = sec (90–x)
tan x
sin x
Supplement Formulas
Pythagorean Identities
sin(π-x) = sinx
2
2
sin
x + cos
x = 1
cos(π-x) = -cosx
2
2
sin
x = 1− cos
x
tan(π-x) = -tanx
2
2
cos
x = 1− sin
x
csc(π-x) = cscx
sec(π-x) = -secx
2
2
sec
x − tan
x = 1
cot(π-x) = -cotx
2
2
sec
x = tan
x + 1
2
2
tan
x = sec
x −1
Addition & Subtraction Formulas
2
2
csc
x − cot
x = 1
cos(x + y) = cos x cos y − sin x sin y
2
2
csc
x = cot
x + 1
cos(x − y) = cos x cos y + sin x sin y
2
2
cot
x = csc
x − 1
sin(x + y) = sin x cos y + cos xsin y
sin(x − y) = sin x cos y − cosx sin y
Symmetry Identities
tan x + tan y
sin(−x) = −sin x
cot(− x) = − cot x
tan( x + y) =
1 − tan x tan y
cos(−x) = cos x
sec(−x) = sec x
tan x − tan y
tan( x − y) =
tan(− x) = − tan x
csc(− x) = − csc x
1 + tan x tan y
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