Before defining the TRIGONOMETRIC FUNCTIONS, we must see how to relate the angles and sides of a right triangle.
A right triangle is composed of a right angle, the angle at C (90 degree, the symbol is small square), and two acute
angles, which are angles less than a right angle. It is conventional
to label the acute angles with Greek letters but for simplicity I will just use English alphabet. For the given figure above the said acute angles are A and B. Always remember that, in Trigonometry we use upper case letter to denote Angle and lower case for side. As for the sides, the side "h", opposite the right angle, is called the hypotenuse. Each acute angle is formed by the hypotenuse and the side adjacent to the angle. Thus, angle B is formed by the hypotenuse h and side a. Angle A is formed by the hypotenuse and side b.
With respect to angle B, though, side b is its opposite side. While side a is the side opposite of Angle A.
The ratios of sides
Any two sides of the triangle will have a ratio -- a relationship -- to one another. It is possible to form six such
ratios: the ratio of the opposite side to the hypotenuse; the adjacent
side to the hypotenuse; and so on. Those six ratios have historical names and abbreviations, with which the student will have to make peace. They are the following.
The reciprocal of sin θ is csc θ ; and vice-versa.
Each ratio moreover is a function
of the acute angle. That is, one quantity is a "function" of another
if its value depends on the value of the other. The circumference of a
circle is a function of the radius, because the size of the
circumference depends on the size of the radius, and when the radius
changes, the circumference also will change. As we will see in the
next Topic, the value of each ratio depends only on the value of the acute angle. That is why we say that those ratios are functions of the acute angle. We call them the trigonometric functions of an acute angle. All of trigonometry is based on the definitions of those functions.
