三角恒等式引用

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

这些都是密切相关的, 但让我们来看看每一种。

角的加减公式

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

半角公式恒等式
$\sin\dfrac\theta2=\pm\sqrt{\dfrac{1-\cos\theta}{2}}$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

使用这个活动点来查看比率的长短是怎么根据角度而变化的。