You have already studied about triangles, and in particular, right triangles, in your
earlier classes. Let us take some examples from our surroundings where right triangles
can be imagined to be formed. For instance :
1. Suppose the students of a school are visiting Qutub Minar. Now, if a student is looking at the top of the Minar, a right triangle can be imagined to be made, as shown in Fig 8.1. Can the student find out the height of the Minar, without actually measuring it?
2. Suppose a girl is sitting on the balcony of her house located on the bank of a river. She is looking down at a flower pot placed on a stair of a temple situated nearby on the other bank of the river.
you have seen some right triangles imagined to be formed in different situations. Let us take a right triangle ABC You have studied the concept of ‘ratio’ in your earlier classes. We now define certain ratios involving the sides of a right triangle, and call them trigonometric ratios.
As you know, for finding the trigonometric ratios, we need to know the lengths of the sides of the triangle. So, let us suppose that AB = 2a.Let us see what happens to the trigonometric ratios of angle A, if it is made smaller and smaller in the right triangle ABC till it becomes zero.
Recall that two angles are said to be complementary if their sum equals 90°. In Δ ABC, right-angled at B, do you see any pair of complementary angles?
You may recall that an equation is called an identity when it is true for all values of the variables involved. Similarly, an equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angle(s) involved.
If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of the angle can be easily determined.The value of sin A or cos A never exceeds 1, whereas the value of sec A or cosec A is always greater than or equal to 1.