Empfehlung zu Trigonometrischer Identität

$\sec(\theta)= \dfrac{1}{\cos(\theta)}$\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

Diese sind alle eng verwandt, aber schauen wir uns jede Art an.

Winkelsummen- und Differenzidentitäten

$\sin(2\theta)=2\sin\theta\cos\theta$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

Halbwinkelidentitäten
$\sin\dfrac\theta2=\pm\sqrt{\dfrac{1-\cos\theta}{2}}$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

Verwende den beweglichen Punkt, um zu sehen, wie sich die Längen der Verhältnisse entsprechend dem Winkel ändern.