Fórmula fundamental da trigonometria

$\sec(\theta)= \dfrac{1}{\cos(\theta)}$\sec, left parenthesis, theta, right parenthesis, equals, start fraction, 1, divided by, cosine, left parenthesis, theta, right parenthesis, end fraction

$\csc(\theta)= \dfrac{1}{\sin(\theta)}$\csc, left parenthesis, theta, right parenthesis, equals, start fraction, 1, divided by, sine, left parenthesis, theta, right parenthesis, end fraction

$\cot(\theta)= \dfrac{1}{\tan(\theta)}$cotangent, left parenthesis, theta, right parenthesis, equals, start fraction, 1, divided by, tangent, left parenthesis, theta, right parenthesis, end fraction

$\tan(\theta)= \dfrac{\sin(\theta)}{\cos(\theta)}$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

$\cot(\theta)= \dfrac{\cos(\theta)}{\sin(\theta)}$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

Elas estão todas relacionadas, mas vamos analisar cada tipo.

$\sin(2\theta)=2\sin\theta\cos\theta$sine, left parenthesis, 2, theta, right parenthesis, equals, 2, sine, theta, cosine, theta
$\cos(2\theta)=2\cos^2\theta-1$cosine, left parenthesis, 2, theta, right parenthesis, equals, 2, cosine, squared, theta, minus, 1
$\tan(2\theta)=\dfrac{2\tan\theta}{1-\tan^2\theta}$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
$\sin\dfrac\theta2=\pm\sqrt{\dfrac{1-\cos\theta}{2}}$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
$\cos\dfrac\theta2=\pm\sqrt{\dfrac{1+\cos\theta}{2}}$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

$\sin(-\theta)=-\sin(\theta)$sine, left parenthesis, minus, theta, right parenthesis, equals, minus, sine, left parenthesis, theta, right parenthesis
$\cos(-\theta)=+\cos(\theta)$cosine, left parenthesis, minus, theta, right parenthesis, equals, plus, cosine, left parenthesis, theta, right parenthesis
$\tan(-\theta)=-\tan(\theta)$tangent, left parenthesis, minus, theta, right parenthesis, equals, minus, tangent, left parenthesis, theta, right parenthesis

$\sin(\theta+2\pi)=\sin(\theta)$sine, left parenthesis, theta, plus, 2, pi, right parenthesis, equals, sine, left parenthesis, theta, right parenthesis
$\cos(\theta+2\pi)=\cos(\theta)$cosine, left parenthesis, theta, plus, 2, pi, right parenthesis, equals, cosine, left parenthesis, theta, right parenthesis
$\tan(\theta+\pi)=\tan(\theta)$tangent, left parenthesis, theta, plus, pi, right parenthesis, equals, tangent, left parenthesis, theta, right parenthesis

Move o ponto para saber como como se alteram as razões trigonométricas em função do ângulo.