razões trigonométricas na circunferência
DESCRIPTION
Estudo da variação das funções trigonométricas no ciclo.TRANSCRIPT
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RAZÕES RAZÕES
TRIGONOMÉTRICAS TRIGONOMÉTRICAS
NA CIRCUNFERÊNCIANA CIRCUNFERÊNCIA
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SENO: ordenada, OS, do ponto P que é a imagem do arco x no ciclo trigonométrico
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Quadrante I 0 < x < rad
2
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Quadrante I 0 < x < rad
2
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Quadrante I 0 < x < rad
2
0 < sen x < 1
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Quadrante II < x < 2
rad
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Quadrante II < x < 2
rad
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Quadrante II < x < 2
rad
0 < sen x < 1
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Quadrante III < x < rad
2
3
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Quadrante III < x < rad
2
3
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Quadrante III < x < rad
2
3
-1 < sen x < 0
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Quadrante IV < x < rad22
3
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Quadrante IV < x < 2
3 rad2
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Quadrante IV < x < 2
3 rad2
-1 < sen x < 0
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COMPORTAMENTO DA FUNÇÃO SENO
QUADRANTE VARIAÇÃO
1º. 1 0 CRESCENTE
2º. 1 0 DECRESCENTE
3º. 0 -1 DECRESCENTE
4º. 0 -1 CRESCENTE
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COSSENO: abscissa, OC, do ponto P que é a imagem do arco x no ciclo trigonométrico
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Quadrante I 0 < x < rad
2
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Quadrante I 0 < x < rad
2
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Quadrante I 0 < x < rad
2
0 < cos x < 1
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Quadrante II < x < 2
rad
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Quadrante II < x < 2
rad
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Quadrante II < x < 2
rad
-1 < cos x < 0
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Quadrante III < x < rad
2
3
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Quadrante III < x < rad
2
3
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Quadrante III < x < rad
2
3
-1 < cos x < 0
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Quadrante IV < x < rad22
3
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Quadrante IV < x < 2
3 rad2
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Quadrante IV < x < 2
3 rad2
0 < cos x < 1
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COMPORTAMENTO DA FUNÇÃO COSSENO
QUADRANTE VARIAÇÃO
1º. 1 0 DECRESCENTE
2º. 0 -1 DECRESCENTE
3º. 0 -1 CRESCENTE
4º. 1 0 CRESCENTE
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TANGENTE: medida algébrica do segmento AT.
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Quadrante I 0 < x < rad
2
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Quadrante I 0 < x < rad
2
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Quadrante I 0 < x < rad
2
tg x > 0
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Quadrante II < x < 2
rad
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Quadrante II < x < 2
rad
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Quadrante II < x < 2
rad
tg x < 0
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rad2
3
Quadrante III < x <
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rad2
3
Quadrante III < x <
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rad2
3
Quadrante III < x <
tg x > 0
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Quadrante IV < x < 2
3rad2
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Quadrante IV < x < 2
3rad2
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rad2
tg x < 0
2
3
Quadrante IV < x <
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COMPORTAMENTO DA FUNÇÃO TANGENTE
QUADRANTE VARIAÇÃO
1º. 0
CRESCENTE
2º. 0 CRESCENTE
3º. 0
CRESCENTE
4º. 0 CRESCENTE
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COTANGENTE: medida algébrica do segmento BC.
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Quadrante I 0 < x < rad
2
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Quadrante I 0 < x < rad
2
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Quadrante I 0 < x < rad
2
cotg x > 0
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Quadrante II < x < 2
rad
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Quadrante II < x < 2
rad
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Quadrante II < x < 2
rad cotg x < 0
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Quadrante III < x < rad
2
3
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Quadrante III < x < rad
2
3
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Quadrante III < x < rad
2
3
cotg x > 0
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Quadrante IV < x < 2
3rad2
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Quadrante IV < x < 2
3rad2
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Quadrante IV < x < 2
3rad2
cotg x < 0
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COMPORTAMENTO DA FUNÇÃO COTANGENTE
QUADRANTE VARIAÇÃO
1º. 0
DECRESCENTE
2º. 0 DECRESCENTE
3º. 0
DECRESCENTE
4º. 0 DECRESCENTE
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SECANTE: medida algébrica do segmento OS.
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Quadrante I 0 < x < rad
2
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Quadrante I 0 < x < rad
2
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Quadrante I 0 < x < rad
2
sec x > 1
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Quadrante II < x < rad
2
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Quadrante II < x < rad
2
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Quadrante II < x < rad
2
sec x < -1
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rad2
3
Quadrante III < x <
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rad2
3
Quadrante III < x <
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rad2
3
Quadrante III < x <
sec x < -1
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Quadrante IV < x < 2
3rad2
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Quadrante IV < x < 2
3rad2
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Quadrante IV < x < 2
3rad2
sec x > 1
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COMPORTAMENTO DA FUNÇÃO SECANTE
QUADRANTE VARIAÇÃO
1º. 1
CRESCENTE
2º. 1 CRESCENTE
3º. 1 DECRESCENTE
4º.+ 1
DECRESCENTE
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COSSECANTE: medida algébrica do segmento OC.
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Quadrante I 0 < x < rad
2
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Quadrante I 0 < x < rad
2
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Quadrante I 0 < x < rad
2
cossec x > 1
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Quadrante II < x < 2
rad
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Quadrante II < x < 2
rad
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Quadrante II < x < 2
rad
cossec x > 1
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rad2
3
Quadrante III < x <
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rad2
3
Quadrante III < x <
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cossec x < -1
Quadrante III < x < rad
2
3
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Quadrante IV < x < rad22
3
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2
3
Quadrante IV < x < rad2
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Quadrante IV < x < rad22
3
cossec x < -1
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COMPORTAMENTO DA FUNÇÃO COSSECANTE
QUADRANTE VARIAÇÃO
1º. 1
DECRESCENTE
2º. + 1
CRESCENTE
3º. 1 CRESCENTE
4º. 1 DECRESCENTE