Trigonometria –

Funções seno e cossenoAula 1

1. a) f x x( ) = − sen

x − sen x

0 0π2

−1

π 032π

1

2π 0

b) f x x( ) cos= −

x − cos x

0 −1

π2

0

π 1

32π

0

2π −1

em21.202

x

f(x)

�_2

� �_2

3 2�

1

1_

�_

�_2

_

�_2

3_

�2_

0

x

f(x)

�_2

_

�_

�

�2_

�_2

3_

�_2

32�

�_2

1

_1

0

1.1

c) f x x( ) | |= sen

f xx x x

x x x( )

, ( )

, ( )=

≥ ≤ ≤− < < <

⎧⎨⎩

sen se sen

sen se sen

0 0

0 2

ππ π

x sen x x − sen x

0 0 π 0

π2

132π

1

π 0 2π 0

d) f x x( ) | |= sen

f xx x

x xf x

x x( )

,

( ),( )

,=

≥− <

⎧⎨⎩

⇒ =≥

−sen se

sen se

sen se

se

0

0

0

n sex x, <⎧⎨⎩ 0

x − sen x x sen x

− 32π

−1 0 0

−π 0π2

1

− π2

1 π 0

32π

−1

em21.202

2�_

3�__2

_

�_

_�

2_

�

3�__2 2�

1

f(x)

_1

x�

2_ 0

x

f(x)

�2_

�_2

3_

�_

�_2

_�_2

� �_2

3 �2

1

0

2.2

e) f x x( ) cos= 3

x cos x 3 cos x

0 1 3

π2

0 0

π −1 −3

32π

0 0

2π 1 3

f) f x x( ) cos= +2

x cos x 2 cos+ x

0 1 3

π2

0 2

π −1 1

32π

0 2

2π 1 3

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�

2__

2� 3�__2

_�

_

_�2

_3�__2

2� x

_3

f(x)

3

0

�

3.3

2. a) f x x( ) = +⎛⎝⎜

⎞⎠⎟

senπ2

x x + π2

sen2

x +⎛⎝⎜

⎞⎠⎟

π

−2π − 32π

1

− 32π 2

2π π= 0

−π − π2

−1

− π2

0 0

0π2

1

π2

22π π= 0

π32π

−1

32π 4

22

π π= 0

2π52π

1

em21.202

x

f(x)

�_2

3 2��2_

�_2

3_

�_

�_2

_�_2

�

1

_1

0

x

f(x)

2��2_

�_

�

1

0

3

4.4

b) g x x( ) cos= −⎛⎝⎜

⎞⎠⎟

π2

x x − π2

cos2

x −⎛⎝⎜

⎞⎠⎟

π

−2π − 52π

0

− 32π − = −4

22

π π 1

−π − 32π

0

− π2

− = −22π π −1

0 − π2

0

π2

0 1

ππ2

0

32π 2

2π π= −1

2π32π

0

em21.202

x

g(x)

1

1_

�2_

�_2

3_

�_

�_2

_

�_2

�

�_2

3

�20

5.5