# Trigonometric functions

Trigonometric elementary functions include 1) sine, 2) cosine, 3) tangent, 4) cosecant, 5) secant, and 6) cotangent.

### Sine

Sine is a trigonometric function defined as the ratio of the opposite side to the hypotenuse in a right-angled triangle:

$$\sin \alpha=\frac{a}{c}$$

where,

a— opposite side of the right-angled triangle;
c— hypotenuse.

### Cosine

Cosine is a trigonometric function defined as the ratio of the adjacent side to the hypotenuse in a right-angled triangle:

$$\cos \alpha=\frac{b}{c}$$

where,

b— adjacent side of the right-angled triangle;
c— hypotenuse.

### Tangent

Tangent is a trigonometric function defined as the ratio of the opposite side to the adjacent side in a right-angled triangle:

$$\tan \alpha=\frac{\sin \alpha}{\cos \alpha}=\frac{a}{b}$$

where,

a— opposite side of the right-angled triangle;
b— adjacent side of the right-angled triangle.

### Cosecant, Secant, and Cotangent

Cosecant, secant, and cotangent are trigonometric functions whose values are, respectively, the reciprocals of the sine, cosine, and tangent of the same argument:

\begin{align} \csc \alpha &=\frac{1}{\sin \alpha}=\frac{c}{a} \\ \\ \sec \alpha &=\frac{1}{\cos \alpha}=\frac{c}{b} \\ \\ \cot \alpha &=\frac{1}{\tan \alpha}=\frac{\cos \alpha}{\sin \alpha}=\frac{b}{a} \\ \end{align}