Saunanaine_Helen Moppel_JUHENDATUD SAUNATEENUSE JA LOODUSMATKA SÜNERGIA_strat...
Exercícios de Trigonometria Resolvidos
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. 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. 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. 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. 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