In trigonometry, we study about the right angled triangle, its angle formed with the base and the relation between its three sides. In maths Trigonometry is the study of the different relations which are formed between the different sides of the right angled triangle. In real life situations we come across certain situations, where we come across the right angled acute Triangles. If we look at a tall building at the top of it, then we find that the building forms a right angled triangle between the building and the flat surface of the earth. In such a situation, if we need to find the height of the building without actually measuring the height of the building. Let us take another example that you are sitting at the balcony of top floor of your house and the house is located over the bank of the river. If there exist a temple with a staircase at the bank of the river then if you look at the edge of the first stair case. If the height at which you are sitting is known and we know that a right angle is formed between the building and the river, then we can easily find the width of the river. This all is by the real life applications of the trigonometry in our life.
In these and many such situations we can find the distance and the height by using many real life mathematical techniques. We learn that word trigonometry is derived from the Greek word “ tri”, which means three, “ gon “ means sides and word “menton “ stands for measure. Trigonometry is the study of the measure of the relationship between the three sides of the right angled triangle. If we talk about the study of some of the ratios of the sides of the right triangle with respect to the acute angles, then these types of ratios are called trigonometric ratios of the angles. Though these ratios are initially formed only for the acute angles, but they can be extended to other larger angles too. Let us take a right angled triangle, right angled at B, and angle CAB is an acute angle. So we say that AC is the Hypotenuse of the right triangle. The trigonometric ratios of the angle A in a right triangle ABC is defined as follows:
Sine of angle A = side opposite to angle A / Hypotenuse
= BC / AC
Cosine of angle A = side adjacent to angle A / Hypotenuse
= AB / AC
Tangent of angle A = side opposite to angle A / side adjacent to angle A
= BC / AB
Cosecant of angle A = 1 / Sine of angle A
= AC / BC
Secant of angle A = 1/ Cosine of angle A
= AC / AB
Cotangent of angle A = 1/ tangent of angle A
= AB / BC
The ratios we have discussed above are also called as Sin A, Cos A, Tan A, Cosec A, Sec A and Cot A. The values of the trigonometric ratios of an angle do not vary with the lengths of the sides of the sides of the Triangles, if we find that the measures of the angles of the triangles remain same.
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