Trigonometria Folha de Apoio

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Trigonometria Folha de Apoio
Identidades básicas
tan x =
cos x
sin x
 
tan x =
cot x
1
 
cot x =
tan x
1
 cot x =
sin x
cos x
 
sec x =
cos x
1
 
csc x =
sin x
1
 
Identidades pitagoreanas
cos x + sin x = 1 sec x − tan x = 1
csc x − cot x = 1
Identidades de ângulo duplo
sin 2x = 2sin x cos x cos 2x = 1 − 2sin x
cos 2x = 2cos x − 1 cos 2x = cos x − sin x
tan 2x =
1 − tan x
2tan x
 
Identidades de soma/diferença
sin s + t = sin s cos t + cos s sin t
sin s − t = sin s cos t − cos s sin t
cos s + t = cos s cos t − sin s sin t
cos s − t = cos s cos t + sin s sin t
tan s + t =
1 − tan s tan t
tan s + tan t
 
tan s − t =
1 + tan s tan t
tan s − tan t
 
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02/02/2026, 19:54 Trigonometria Folha de Apoio
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Identidades de soma para produto
cos s cos t =
2
cos s − t + cos s + t
 
sin s sin t =
2
cos s − t − cos s + t
 
sin s cos t =
2
sin s + t + sin s − t
 
cos s sin t =
2
sin s + t − sin s − t
 
Identidades de ângulo triplo
sin 3x = −sin x + 3cos x sin x
sin 3x = −4sin x + 3sin x
cos 3x = cos x − 3sin x cos x
cos 3x = 4cos x − 3cos x
tan 3x =
1 − 3tan x
3tan x − tan x
 
cot 3x =
1 − 3cot x
3cot x − cot x
 
Imagens de função
y = sin x −1 ≤ y ≤ 1
y = cos x −1 ≤ y ≤ 1
y = tan x −∞