Conteúdo principal
Trigonometria
Assunto: Trigonometria > Tema 4
Lição 5: Simplificação de uma expressão trigonométrica- Cálculo de valores trigonométricos a partir de identidades da adição de ângulos
- Calcular valores trigonométricos a partir de identidades da adição de ângulos
- Usar as identidades trigonométricas de adição de ângulos: cálculo das medidas dos lados
- Usar as identidades trigonométricas de adição de ângulos: manipulação de expressões
- Simplificação de uma expressão trigonométrica
- Fórmula fundamental da trigonometria
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Fórmula fundamental da trigonometria
Procurar e compreender todas as tuas identidades trigonométricas favoritas
Fórmulas sobre o inverso dos valores das funções
\sec, left parenthesis, theta, right parenthesis, equals, start fraction, 1, divided by, cosine, left parenthesis, theta, right parenthesis, end fraction
\csc, left parenthesis, theta, right parenthesis, equals, start fraction, 1, divided by, sine, left parenthesis, theta, right parenthesis, end fraction
cotangent, left parenthesis, theta, right parenthesis, equals, start fraction, 1, divided by, tangent, left parenthesis, theta, right parenthesis, end fraction
tangent, left parenthesis, theta, right parenthesis, equals, start fraction, sine, left parenthesis, theta, right parenthesis, divided by, cosine, left parenthesis, theta, right parenthesis, end fraction
cotangent, left parenthesis, theta, right parenthesis, equals, start fraction, cosine, left parenthesis, theta, right parenthesis, divided by, sine, left parenthesis, theta, right parenthesis, end fraction
\csc, left parenthesis, theta, right parenthesis, equals, start fraction, 1, divided by, sine, left parenthesis, theta, right parenthesis, end fraction
cotangent, left parenthesis, theta, right parenthesis, equals, start fraction, 1, divided by, tangent, left parenthesis, theta, right parenthesis, end fraction
tangent, left parenthesis, theta, right parenthesis, equals, start fraction, sine, left parenthesis, theta, right parenthesis, divided by, cosine, left parenthesis, theta, right parenthesis, end fraction
cotangent, left parenthesis, theta, right parenthesis, equals, start fraction, cosine, left parenthesis, theta, right parenthesis, divided by, sine, left parenthesis, theta, right parenthesis, end fraction
Fórmula fundamental da trigonometria e suas derivadas
sine, squared, left parenthesis, theta, right parenthesis, plus, cosine, squared, left parenthesis, theta, right parenthesis, equals, 1, squared
tangent, squared, left parenthesis, theta, right parenthesis, plus, 1, squared, equals, \sec, squared, left parenthesis, theta, right parenthesis
cotangent, squared, left parenthesis, theta, right parenthesis, plus, 1, squared, equals, \csc, squared, left parenthesis, theta, right parenthesis
Fórmulas para somas, diferenças, múltiplos e frações de ângulos
Elas estão todas relacionadas, mas vamos analisar cada tipo.
Fórmulas para somas e diferenças de ângulos
sine, left parenthesis, theta, plus, \phi, right parenthesis, equals, sine, theta, cosine, \phi, plus, cosine, theta, sine, \phi
sine, left parenthesis, theta, minus, \phi, right parenthesis, equals, sine, theta, cosine, \phi, minus, cosine, theta, sine, \phi
cosine, left parenthesis, theta, plus, \phi, right parenthesis, equals, cosine, theta, cosine, \phi, minus, sine, theta, sine, \phi
cosine, left parenthesis, theta, minus, \phi, right parenthesis, equals, cosine, theta, cosine, \phi, plus, sine, theta, sine, \phi
sine, left parenthesis, theta, minus, \phi, right parenthesis, equals, sine, theta, cosine, \phi, minus, cosine, theta, sine, \phi
cosine, left parenthesis, theta, plus, \phi, right parenthesis, equals, cosine, theta, cosine, \phi, minus, sine, theta, sine, \phi
cosine, left parenthesis, theta, minus, \phi, right parenthesis, equals, cosine, theta, cosine, \phi, plus, sine, theta, sine, \phi
tangent, left parenthesis, theta, minus, \phi, right parenthesis, equals, start fraction, tangent, theta, minus, tangent, \phi, divided by, 1, plus, tangent, theta, tangent, \phi, end fraction
Fórmulas para o dobro de um ângulo
sine, left parenthesis, 2, theta, right parenthesis, equals, 2, sine, theta, cosine, theta
cosine, left parenthesis, 2, theta, right parenthesis, equals, 2, cosine, squared, theta, minus, 1
tangent, left parenthesis, 2, theta, right parenthesis, equals, start fraction, 2, tangent, theta, divided by, 1, minus, tangent, squared, theta, end fraction
cosine, left parenthesis, 2, theta, right parenthesis, equals, 2, cosine, squared, theta, minus, 1
tangent, left parenthesis, 2, theta, right parenthesis, equals, start fraction, 2, tangent, theta, divided by, 1, minus, tangent, squared, theta, end fraction
Fórmulas para metade de um ângulo
sine, start fraction, theta, divided by, 2, end fraction, equals, plus minus, square root of, start fraction, 1, minus, cosine, theta, divided by, 2, end fraction, end square root
cosine, start fraction, theta, divided by, 2, end fraction, equals, plus minus, square root of, start fraction, 1, plus, cosine, theta, divided by, 2, end fraction, end square root
sine, start fraction, theta, divided by, 2, end fraction, equals, plus minus, square root of, start fraction, 1, minus, cosine, theta, divided by, 2, end fraction, end square root
cosine, start fraction, theta, divided by, 2, end fraction, equals, plus minus, square root of, start fraction, 1, plus, cosine, theta, divided by, 2, end fraction, end square root
Fórmulas sobre simetria e periodicidade
sine, left parenthesis, minus, theta, right parenthesis, equals, minus, sine, left parenthesis, theta, right parenthesis
cosine, left parenthesis, minus, theta, right parenthesis, equals, plus, cosine, left parenthesis, theta, right parenthesis
tangent, left parenthesis, minus, theta, right parenthesis, equals, minus, tangent, left parenthesis, theta, right parenthesis
sine, left parenthesis, theta, plus, 2, pi, right parenthesis, equals, sine, left parenthesis, theta, right parenthesis
cosine, left parenthesis, theta, plus, 2, pi, right parenthesis, equals, cosine, left parenthesis, theta, right parenthesis
tangent, left parenthesis, theta, plus, pi, right parenthesis, equals, tangent, left parenthesis, theta, right parenthesis
cosine, left parenthesis, minus, theta, right parenthesis, equals, plus, cosine, left parenthesis, theta, right parenthesis
tangent, left parenthesis, minus, theta, right parenthesis, equals, minus, tangent, left parenthesis, theta, right parenthesis
sine, left parenthesis, theta, plus, 2, pi, right parenthesis, equals, sine, left parenthesis, theta, right parenthesis
cosine, left parenthesis, theta, plus, 2, pi, right parenthesis, equals, cosine, left parenthesis, theta, right parenthesis
tangent, left parenthesis, theta, plus, pi, right parenthesis, equals, tangent, left parenthesis, theta, right parenthesis
Fórmulas em relação ao ângulo complementar
\csc, theta, equals, \sec, left parenthesis, start fraction, pi, divided by, 2, end fraction, minus, theta, right parenthesis
Apêndice: todas as razões trigonométricas no círculo trigonométrico
Move o ponto para saber como como se alteram as razões trigonométricas em função do ângulo.
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