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}
See also:
Trigonometric Functions FAQ
What are the basic trigonometric functions?
The basic trigonometric functions are sine, cosine, tangent, cosecant, secant, and cotangent.
How are sine, cosine, and tangent defined?
They are defined as ratios of the sides of a right triangle.
