This document provides definitions and properties for trigonometric functions including sine, cosine, and tangent. It defines the domains and ranges of sine, cosine, and tangent. Examples of trigonometric ratios are given for common angles like 30, 45, 60, and 90 degrees. Trigonometric identities are also listed, such as the sine and cosine of sums and differences of angles.

1. An´lise Matem´tica
a a Pedro Dias
1 Seno
y
1
π π
x sin(x) : − , −→ [−1, 1]
2 2
−π π
2 2
−1 sin(−x) = −sin(x)
2 Co-seno
y
1
0 x cos(x) : [0, π] −→ [−1, 1]
π
2 π
cos(x) = cos(−x)
−1
3 Tangente
y
1
π π
x tan(x) : − , −→ R
2 2
−π π
2 2
−1 sin(x)
tan(x) = , cos(x) = 0
cos(x)
cotan(x) : ]0, π[ −→ R
y
1 tan(x) π o π o π o π o
α 6 (30 ) 4 (45 ) 3 (60 ) 2 (90 )
√
1 1 3 sqrt1
sin(x) sin(α) 2
√
2 2 2 =1
α √
3 1 1
x cos(α) 2
√
2 2 0
−1 cos(x) 1
1
√
tan(α) √
3
1 3 − inf
2 2
sin (α) + cos (α) = 1
−1 tan2 (α) + 1 = sec2 (α)
sin(α ± β) = sin(α) • cos(β) ± sin(β) • cos(α)
1

2. An´lise Matem´tica
a a Pedro Dias
cos(α ± β) = sin(α) • cos(β) ∓ sin(β) • cos(α)
2