Przypomnienie tożsamości trygonometrycznych

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

Są ze sobą ściśle powiązane, ale dla porządku zajmiemy się każdym rodzajem oddzielnie.

Wzory na funkcje trygonometryczne sumy i różnicy kątów

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

Funkcje trygonometryczne połówki kąta
$\sin\dfrac\theta2=\pm\sqrt{\dfrac{1-\cos\theta}{2}}$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

Zmieniaj kąt przesuwając zielony punkt na okręgu i obserwuj jak zmieniają się długości odcinków, równe różnym funkcjom trygonometrycznym.