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Trigo ppt by mohit manchanda

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trignometry fundas

trignometry fundas


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  • 1. The word trigonometry is derived from Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides) and metron (meaning measure). In fact , The earliest known work on trigonometry was recorded in Egypt and Babylon. Early astronomers used to find out the distance of the stars and planet s from the Earth. Introductio n
  • 2. Introduction To Trigonometry There is no perhaps nothing which so occupies the middle position of mathematics as trigonometry. -J.F. Herbart(1890)
  • 3. •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 could be imagined to be made.
  • 4. • Suppose a girl sitting on the balcony of her house located on the bank of a river. She is looking down at a flower pot placed on stair of a temple situated nearby on the other bank of the river. A right triangle is imagined to be made in this situation.
  • 5. Trigonometric ratios
  • 6. The trigonometric ratios of the angle A in the right triangle ABC see in fig. •Sin of A =side opposite to angle A =BC hypotenuse AC •Cosine of A =side adjacent to angle A =AB hypotenuse AC •Tangent of A =side opposite to angle A =BC side adjacent to angle A AB C A B
  • 7. Cosecant of A = 1 = hypotenuse = AC sin of A side opposite to angle A BC Secant of A = 1 = hypotenuse = AC sin of A side adjacent to angle a AB Cotangent of A= 1 =side adjacent to angle A= AB tangent of A side opposite to angle A BC C A B
  • 8. These are some easy method to learn these formulas: •Pandit Badri Prasad Har Har Bhole Sona Chandi Tole •Pakistan Bhuka Pyasa Hindustan Hara Bhara. S C T P B P H H B
  • 9. The first use of the idea of ‘sine’ in the way we use it today was in the work ‘Aryabhatiyam’ by Aryabhatta, in A.D. 500. Aryabhatta used the word ardha-jiva for the half-chord, which shortened to jya or jiva. When it was translated into Latin, the word jiva was translated into sinus, which means curve. Sin Sin Sin Sin Sin Sin Sin Sin Sin Sin Sin Sin Sin Sin Sin Sin ORIGIN OF ‘SINE’
  • 10. Foundation of COSINE & TANGENT The origin of terms cosinecosine and tangenttangent was much later. The cosine function arose from the need to compute the sine of the complementary angle. AryabhataAryabhata called it kotijyakotijya. The name cosinus originated with Edmund GunterEdmund Gunter. In 1674, the English mathematician Sir Jonas MooreSir Jonas Moore first use the abbreviated notation coscos.
  • 11. TRIGONOMETR IC RATIOS OF SOME SPECIFIC ANGLES
  • 12. Trigonometric ratios of some specific angles
  • 13. Trigonometry ratios of complimentary angles Recall two angles are said to be complimentary if their sum equals 90°.Sin ( 90° - A) = cos A, Tan (90°- A ) = cot A, Sec (90° - A ) = cosec A, Cos ( 90° - A ) = sin A, Cot (90° - A) = tan A, Cosec (90° - A ) = sec A.
  • 14. WHAT ARE TRIGONOMETRIC IDENTITIES ???? An equation involving trigonometric ratios of an angle is called a Trigonometric Identitity, if it is true for all values of the angle(s) involved. Trigonometric identities are ratios and
  • 15. Trigonometric identitiesTrigonometric identities • cos²A + sin²A = 1cos²A + sin²A = 1 • 1 + tan²A = sec²A (1 + tan²A = sec²A (0*≤ A ≤ 90*)0*≤ A ≤ 90*) • cot²A + 1 = cosec²A (cot²A + 1 = cosec²A (0* < A ≤ 90*)0* < A ≤ 90*)
  • 16. OTHER USEFUL IDENTITIES • Sin = 1/cosecθ θ • Cos = 1/secθ θ • Tan = 1/cotθ θ • Cosec = 1/sinθ θ • Sec = 1/cosθ θ • Tan = 1/cotθ θ
  • 17. The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer. Line of sight
  • 18. ANGLE OF ELEVATION When a person looks at something above his or her location, the angle between the line of sight and the horizontal is called the angle of elevation. In this case, the line of sight is “elevated” above the horizontal.
  • 19. ANGLE OF DEPRESSION When a person looks at something below his or her location, the angle between the line of sight and the horizontal is called the angle of depression. In this case, the line of sight is “depressed” below the horizontal.