In mathematics, the trigonometric functions are a set of functions which relate angles to the sides of a right triangle. There are many trigonometric functions, the 3 most common being sine, cosine, tangent, followed by cotangent, secant and cosecant. The last three are called reciprocal trigonometric functions, because they act as the reciprocals of other functions. Secant and cosecant are rarely used.
Function | Abbreviation | Relation (Radians) |
Sine | sin | \displaystyle{ \sin \theta = \cos \left(\frac{\pi}{2} - \theta \right) \, } |
Cosine | cos | \displaystyle{ \cos \theta = \sin \left(\frac{\pi}{2} - \theta \right)\, } |
Tangent | tan (or tg) | \displaystyle{ \tan \theta = \frac{\sin \theta}{\cos \theta} = \cot \left(\frac{\pi}{2} - \theta \right) = \frac{1}{\cot \theta} \, } |
Cotangent | cot (or ctg) | \displaystyle{ \cot \theta = \frac{\cos \theta}{\sin \theta} = \tan \left(\frac{\pi}{2} - \theta \right) = \frac{1}{\tan \theta} \, } |
Secant | sec | \displaystyle{ \sec \theta = \frac{1}{\cos \theta} = \csc \left(\frac{\pi}{2} - \theta \right) \, } |
Cosecant | csc (or cosec) | \displaystyle{ \csc \theta =\frac{1}{\sin \theta} = \sec \left(\frac{\pi}{2} - \theta \right) \, } |