When an artist wants to draws a picture then he/she always draw the replica of that object. Say, replica of the great Taj-Mahal of Agra (India) or statue of Liberty and so on. He/She, fix the drawing paper on the table. Fixes the distance between paper and his/her eye-site. Then he/she takes all required measurements of the object (Taj-Mahal/Statue of Liberty) on pencil by holding it between his/her eye-site and the object by locating the bottom of an object at the lower side of the pencil and the tip of an object at the tip of the pencil. Using these distances on the pencil he/she fixes the height, width and all other dimensions of an object on the drawing paper. Here, using the properties of similarities in right angled triangle, an artist or an architecture
Mathematically, we can say that [BC/AB] = [MN/AM] .
Now let us study some thing about right angled triangle. In the adjacent figure triangle ABC is the right angled triangle. < ABC is right angle, so the side opposite to right angle is known as hypotenuse. Considering < A is our angle of the right angled triangle, then side AB is known as side adjacent to angle A and the side BC is the side opposite to angle A.
Details of trigonometric ratios:
1) sin A ------ sine of angle A
2) cos A ------ co-sine of angle A
3) tan A ------ tangent of angle A
4) csc A ------ co-secant of angle A (generally written as cosec A)
5) sec A ------ secant of angle A
6) cot A ------ co-tangent of angle A
Now we will define all six trigonometric ratios as follows:
1) sin A = BC/AC = opposite / hypotenuse
2) cos A = AB/AC = adjacent / hypotenuse
3) tan A = BC/AB = opposite / adjacent
4) csc A = AC/BC = hypotenuse / opposite
5) sec A = AC/AB = hypotenuse / adjacent
6) cot A = AB/BC = adjacent / opposite
Now study all basic concepts of trigonometry as discussed above and do at least two experiments as stated bellow.
1) Define all trigonometric ratios for an angle C of above triangle ABC .
2) Observe the adjacent figure and write down all the trigonometric ratios.