几何-三角形及三角函数

几何-三角形及三角函数

flyfish 2015-12-3 笔记

等腰三角形（isosceles triangle）
等边三角形（equilateral triangle）
直角三角形（right triangle）
直角（right angle）。
直角三角形90°角所对的边称为斜边（hypotenuse），
另外两条边称为直角边（leg）。
相似三角形（similar triangles）

sine sin opposite / hypotenuse
cosine cos adjacent / hypotenuse
tangent tan opposite / adjacent 
cotangent cot adjacent / opposite
secant sec hypotenuse / adjacent 
cosecant csc hypotenuse / opposite

斜边（hypotenuse）
对边（opposite）
邻边（adjacent)

sine sin

$${\displaystyle \sin A={\frac {\textrm {opposite}}{\textrm {hypotenuse}}}}$$

cosine cos

$${\displaystyle \cos A={\frac {\textrm {adjacent}}{\textrm {hypotenuse}}}}$$

tangent tan (or tg)

$${\displaystyle \tan A={\frac {\textrm {opposite}}{\textrm {adjacent}}}}$$

tangent tan (or tg)

$${\displaystyle \tan A={\frac {\sin A}{\cos A}}={\frac {\textrm {opposite}}{\textrm {adjacent}}}}$$

sine sin

$${\displaystyle \sin \theta =\cos \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\csc \theta }}} \sin \theta =\cos \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\csc \theta }}$$

cosine cos

$${\displaystyle \cos \theta =\sin \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\sec \theta }}\,} \cos \theta =\sin \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\sec \theta }}\,$$
tangent tan (or tg)

$${\displaystyle \tan \theta ={\frac {\sin \theta }{\cos \theta }}=\cot \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\cot \theta }}} \tan \theta ={\frac {\sin \theta }{\cos \theta }}=\cot \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\cot \theta }}$$
cotangent cot (or cotan or cotg or ctg or ctn)

$${\displaystyle \cot \theta ={\frac {\cos \theta }{\sin \theta }}=\tan \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\tan \theta }}} \cot \theta ={\frac {\cos \theta }{\sin \theta }}=\tan \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\tan \theta }}$$

secant sec

$${\displaystyle \sec \theta =\csc \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\cos \theta }}} \sec \theta =\csc \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\cos \theta }}$$

cosecant csc (or cosec)

$$csc(x)={1 \over sin(x)},sec(x)={1 \over cos(x)},cot(x)={1 \over tan(x)}$$