MS380 - Aula Complementar Trigonometria

MS380 - Aula Complementar Trigonometria
MS380 - Aula Complementar
Trigonometria
Abel Soares Siqueira
Laércio Luı́s Vendite
MS380 - Aula Complementar Trigonometria
Trigonometria
Trigonometria
a
α
b
c
a
b
cos α =
a
c
sin α
tan α = =
b
cos α
sin α =
c
MS380 - Aula Complementar Trigonometria
Trigonometria
Trigonometria
a
θ
b
π
−α
2
b
sin θ =
a
c
cos θ =
a
sin θ
b
tan θ = =
c
cos θ
θ=
c
MS380 - Aula Complementar Trigonometria
Trigonometria
Trigonometria
a
c
α
b
sin(π/2 − α) = cos(α)
cos(π/2 − α) = sin(α)
1
tan(π/2 − α) =
tan(α)
MS380 - Aula Complementar Trigonometria
Trigonometria
Trigonometria
sin α
α
cos α
tan α
MS380 - Aula Complementar Trigonometria
Trigonometria
Trigonometria
sin α
sin(π + α) = − sin(α)
α
cos α
cos(π + α) = − cos(α)
tan α
tan(π + α) = tan(α)
MS380 - Aula Complementar Trigonometria
Trigonometria
Trigonometria
sin α
sin(π − α) = sin(α)
α
cos α
cos(π − α) = − cos(α)
tan α
tan(π − α) = − tan(α)
MS380 - Aula Complementar Trigonometria
Trigonometria
Trigonometria
sin α
sin(π/2 + α) = cos(α)
α
cos α
cos(π/2 + α) = − sin(α)
tan α
tan(π/2 + α) = −
1
tan(α)
MS380 - Aula Complementar Trigonometria
Trigonometria
Trigonometria
sin(a + b) = sin(a) cos(b) + sin(b) cos(a)
cos(a + b) = cos(a) cos(b) − sin(a) sin(b)
tan(a + b) =
tan(a) + tan(b)
1 − tan(a) tan(b)