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