Trignometry in daily life

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Trignometry in daily life

  1. 1. USE OF TRIGONOMETRY IN REAL LIFE SUPREIYA CLASS : X - A
  2. 2. 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.
  3. 3. ORIGIN OF ‘SINE’ “Trigonometry is not the work of any one person or nation. Its history spans thousands of years and has touched every major civilization .”  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 ’ . Aryabhata A.D. 476-550
  4. 4. COSINE AND TANGENT  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’ Edmund Gunter (1581 –1626)
  5. 5. THE TRIGONOMETRIC RATIOS Abbr. Descriptio n Sine sin Opposite Cosine cos Tangent tan Cotangent The Cosecant, Secant, and Cotangent are the Reciprocals of the Sine, Cosine,and Tangent respectively . Function cot Secant Note: The formulas provided are in respect to the picture. sec Cosecan cosec t Hypotenus e Adjacent Hypotenus e Opposite Adjacent Adjacent Opposite Hypotenus e Adjacent Hypotenus e
  6. 6. THE TRIGONOMETRIC VALUES Angle A 0o 30o 45o 60o 90o sin A 0 1 1 √3 1 1 2 √3 √2 1 2 1 0 0 2 1 √2 1 2 √3 √3 2 √2 2 2 √2 √3 2 √3 √3 1 1 cos A tan A cosec A sec A cot A Not Defined 1 Not Defined √3 Not Defined 1 Not Defined 0
  7. 7. HOW TO USE TRIGONOMETRY IN REAL The LIFE given is elaborated as follows: project ?  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
  8. 8. 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 !!
  9. 9. 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 : Perpendicular (opposite) Hypotenuse  We already know that this value is equal to sin.  Now the values I got were: Perpendicular = 6 mts. Hypotenuse = 12mts.
  10. 10. THERE’S THE ANSWER!!!  Sin A = Perpendicular Hypotenuse = (Putting the Values) 6 12 Sin A = 1 2 Sin A = Sin 30 o Angle of Elevation = 30o
  11. 11. THANK YOU

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