What are trigonometric functions?

Answer 1

Let's look at right triangles for a moment. In any right triangle, the hypotenuse is the side opposite the right angle. There exist three ratios (and their inverses) as regards the length of the sides of the right triangle. These are opposite/hypotenuse (called the sine function), adjacent/hypotenuse (called the cosine function), and opposite/adjacent (called the tangent function). The inverse of the sine is the cosecant, the inverse of the cosine is the secant, and the inverse of the tangent is the cotangent. The abbreviations for these functions are, sin, cos, tan, csc, sec and cot, respectively.

What is underneath this idea is that for any (every!) right triangle, there is a fundamental relationship or ratio between the lengths of the sides for all triangles with the same angles. For instance, if we have a triangle with interior angles of 30 and 60 degrees (in addition to the right angle), regardless of what size it is, the ratio of the lengths of the sides is always the same. And the trigonometric functions express the ratios of the lengths of the sides.