Exercícios de Trigonometria Resolvidos
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Transcript of Exercícios de Trigonometria Resolvidos
![Page 1: Exercícios de Trigonometria Resolvidos](https://reader031.fdocumentos.tips/reader031/viewer/2022013111/55939a291a28ab8b1a8b46fa/html5/thumbnails/1.jpg)
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
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![Page 2: Exercícios de Trigonometria Resolvidos](https://reader031.fdocumentos.tips/reader031/viewer/2022013111/55939a291a28ab8b1a8b46fa/html5/thumbnails/2.jpg)
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
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![Page 3: Exercícios de Trigonometria Resolvidos](https://reader031.fdocumentos.tips/reader031/viewer/2022013111/55939a291a28ab8b1a8b46fa/html5/thumbnails/3.jpg)
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
em21.202
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![Page 4: Exercícios de Trigonometria Resolvidos](https://reader031.fdocumentos.tips/reader031/viewer/2022013111/55939a291a28ab8b1a8b46fa/html5/thumbnails/4.jpg)
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
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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
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g(x)
1
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