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# Exercícios de Trigonometria Resolvidos

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### Exercícios de Trigonometria Resolvidos

1. 1. Trigonometria – Funções seno e cosseno Aula 1 1. a) f ( x ) = − sen x x − sen x 0 π 2 π 3π 2 2π 0 −1 0 1 0 f(x) 1 _ 2p _ 3p _ 2 _ p __ p 2 p _ 2 0 p 3p _ 2 2p x _1 b) f ( x ) = − cos x x − cos x 0 π 2 −1 π 3π 2 1 0 2π 0 −1 f(x) 1 _ _ 3p _ 2 2p _p __ p 2 p _ 2 0 _1 1.1 em21.202 p 3p _ 2 2p x
2. 2. c) f ( x ) = | sen x | ⎧sen x , se sen x ≥ 0 (0 ≤ x ≤ π ) f (x ) = ⎨ ⎩ − sen x , se sen x < 0 ( π < x < 2π ) x sen x x − sen x 0 π 2 0 π 3π 2 0 1 π 0 1 2π 0 f(x) 1 _ _ 3p _ 2 2p _p __ p 2 p _ 2 0 p 3p _ 2 2p x d) f ( x ) = sen | x | ⎧sen x , se x ≥ 0 ⎧sen x , se x ≥ 0 f (x ) = ⎨ ⇒ f (x ) = ⎨ ⎩ − sen x , se x < 0 ⎩sen( −x ), se x < 0 − sen x x sen x −1 0 0 −π 0 π 2 1 π 2 1 π 0 3π 2 −1 x 3π 2 − − f(x) 1 _ 2p _ 3p __ 2 _p _p _ 0 2 _1 2.2 em21.202 p _ 2 p 3p __ 2 2p x
3. 3. e) f ( x ) = 3 cos x x 0 π 2 cos x 3 cos x 1 3 0 0 π 3π 2 −1 −3 0 0 2π 1 3 f(x) 3 _ 2p _ 3p __ 2 _p __ p p _ 2 0 2 _ 3 f) f ( x ) = 2 + cos x x cos x 2 + cos x 0 π 2 1 3 0 2 π 3π 2 −1 1 0 2 2π 1 3 3.3 em21.202 p 3p __ 2 2p x
4. 4. f(x) 3 1 _p _ 2p p 0 2p x π⎞ ⎛ 2. a) f ( x ) = sen⎜ x + ⎟ ⎝ 2⎠ x −2π 3π 2 − −π − π 2 3π − 2 2π = π 2 π − 2 π⎞ ⎛ sen⎜ x + ⎟ ⎝ 2⎠ 0 0 π 2 1 x + π 2 0 π 2 π 3π 2 2π 1 0 −1 2π = π 2 3π 2 4π = 2π 2 5π 2 0 −1 0 1 f(x) 1 _ 2p _ 3p _ 2 _p __ p 2 0 p _ 2 _1 4.4 em21.202 p 3p _ 2 2p x
5. 5. π⎞ ⎛ b) g ( x ) = cos⎜ x − ⎟ ⎝ 2⎠ π 2 5π − 2 4π − = −2 π 2 3π − 2 2π − = −π 2 π − 2 π⎞ ⎛ cos⎜ x − ⎟ ⎝ 2⎠ π 2 0 1 π π 2 0 x − x −2π 3π 2 − −π − π 2 0 3π 2 2π 0 1 0 −1 0 2π = π 2 3π 2 −1 0 g(x) 1 _ 2p _ 3p _ 2 _p __ p 2 0 _1 5.5 em21.202 p _ 2 p 3p _ 2 2p x