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Conteúdo principal

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

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
tangent, left parenthesis, theta, plus, \phi, right parenthesis, equals, start fraction, tangent, theta, plus, tangent, \phi, divided by, 1, minus, tangent, theta, tangent, \phi, end fraction
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
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
tanθ2=±1cosθ1+cosθ=       1cosθsinθ=       sinθ1+cosθ\begin{aligned} \tan\dfrac{\theta}{2}&=\pm\sqrt{\dfrac{1-\cos\theta}{1+\cos\theta}}\\ \\ &=~~~~~~~\dfrac{1-\cos\theta}{\sin\theta}\\ \\ &=~~~~~~~\dfrac{\sin\theta}{1+\cos\theta}\end{aligned}

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

Fórmulas em relação ao ângulo complementar

sine, theta, equals, cosine, left parenthesis, start fraction, pi, divided by, 2, end fraction, minus, theta, right parenthesis
cosine, theta, equals, sine, left parenthesis, start fraction, pi, divided by, 2, end fraction, minus, theta, right parenthesis
tangent, theta, equals, cotangent, left parenthesis, start fraction, pi, divided by, 2, end fraction, minus, theta, right parenthesis
cotangent, theta, equals, tangent, left parenthesis, start fraction, pi, divided by, 2, end fraction, minus, theta, right parenthesis
\sec, theta, equals, \csc, left parenthesis, start fraction, pi, divided by, 2, end fraction, minus, theta, right parenthesis
\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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