Trigonometric functions

Posted by : wasin singhanan วันอังคารที่ 18 กันยายน พ.ศ. 2555

Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions) are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

Right-angled triangle definitions

Function	Abbreviation	Description	Identities (using radians)
Sine	sin	opposite / hypotenuse	$\sin \theta = \cos \left(\frac{\pi}{2} - \theta \right) = \frac{1}{\csc \theta}$
Cosine	cos	adjacent / hypotenuse	$\cos \theta = \sin \left(\frac{\pi}{2} - \theta \right) = \frac{1}{\sec \theta}\,$
Tangent	tan (or tg)	opposite / adjacent	$\tan \theta = \frac{\sin \theta}{\cos \theta} = \cot \left(\frac{\pi}{2} - \theta \right) = \frac{1}{\cot \theta}$
Cotangent	cot (or cotan or cotg or ctg or ctn)	adjacent / opposite	$\cot \theta = \frac{\cos \theta}{\sin \theta} = \tan \left(\frac{\pi}{2} - \theta \right) = \frac{1}{\tan \theta}$
Secant	sec	hypotenuse / adjacent	$\sec \theta = \csc \left(\frac{\pi}{2} - \theta \right) = \frac{1}{\cos \theta}$
Cosecant	csc (or cosec)	hypotenuse / opposite	$\csc \theta = \sec \left(\frac{\pi}{2} - \theta \right) = \frac{1}{\sin \theta}$