TRIGONOMETRY IN : TRIGONOMETRY IN BHARAT BIJUKUMAR
CLASS : X - A USE OF REAL LIFE WHAT IS TRIGONOMETRY? : WHAT IS TRIGONOMETRY? Trigonometry in basic words is the mathematics of triangles and trigonometric functions.
The word “Trigonometry” comes from the Greek words: ‘Trigonon’ meaning ‘triangle’ and ‘metron’ meaning a ‘measure’.
In a broader sense, trigonometry is that branch if mathematics which deals with the measurement of the sides and the angles of a triangle and the problems allied with angles. ORIGIN OF ‘SINE’ : ORIGIN OF ‘SINE’ The first use of the idea of ‘sine’ in the way we use it today was in the work Aryabhatiyam by Aryabhata in A.D. 500.
Aryabhata used the word ‘ardha-jya’ for the half chord which came to be known as ‘jiva’ in due course.
Later, ‘jiva’ came to be known as ‘sinus’ and later as ‘sine’.
An English Professor Edmund Gunter (1581-1626) first used the abbreviated notation ‘sin’ . “Trigonometry is not the work of any one person or nation. Its history spans thousands of years and has touched every major civilization.” Aryabhata
A.D. 476-550 Slide 4: The origin of the terms ‘cosine’ and ‘tangent’ was much later. The cosine function arose from the need to compute the sine of the complementary angle.
Aryabhata called ‘kotijya’.
The name cosinus originated with Edmund Gunter. In 1674, the English Mathematician Sir Jonas Moore first used the abbreviated notation ‘cos’ COSINE AND TANGENT Edmund Gunter
(1581 –1626) THE TRIGONOMETRIC RATIOS : THE TRIGONOMETRIC RATIOS Note: The formulas provided are in respect to the picture. The Cosecant, Secant, and Cotangent
are the Reciprocals of
the Sine, Cosine,and Tangent respectively . THE TRIGONOMETRIC VALUES : THE TRIGONOMETRIC VALUES HOW TO USE TRIGONOMETRY IN REAL LIFE ? : HOW TO USE TRIGONOMETRY IN REAL LIFE ? Objective : To find the angle of elevation
of a room .
Knowledge Required : 1.Trigonometric Ratios
2. Trigonometric Values (acute angles)
Materials Required : 1. A meter stick
2. A measuring tape The project given is elaborated as follows: PERFORMING THE TASK !! : PERFORMING THE TASK !! Take the meter stick and put it horizontally on the wall to measure the length .
Now, with the help of an adult measure the diagonal distance (hypotenuse) of your room.
Record the length in centimeters and convert it into meters.
Take the ratio of the length of the stick to the diagonal distance to your room.
Use the trigonometric ratios to find out the angle of elevation of your room !! THE MUCH AWAITED RESULT : THE MUCH AWAITED RESULT I performed the activity mentioned and since I took the ratio of wall to the diagonal my ratio was as follows :
We already know that this value is equal to sin.
Now the values I got were:
Perpendicular = 6 mts.
Hypotenuse = 12mts. THERE’S THE ANSWER!!! : THERE’S THE ANSWER!!! Sin A = Perpendicular
= 6 (Putting the Values)
Sin A = 1
Sin A = Sin 30o Angle of Elevation = 30o Slide 11: THANK YOU