The word trigonometry is derived from
Greek words ‘tri’ (meaning three), ‘gon’
(meaning sides) and metron (meaning
measure...
Introduction To Trigonometry
There is no perhaps nothing which so occupies the
middle position of mathematics as trigonome...
•Suppose the students of a school are
visiting Qutub Minar. Now, if a student is
looking at the top of the Minar a right
t...
• 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 p...
Trigonometric
ratios
The trigonometric ratios of the angle A in the right
triangle ABC see in fig.
•Sin of A =side opposite to angle A =BC
hypo...
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 a...
These are some easy method to learn these formulas:
•Pandit Badri Prasad Har Har Bhole Sona Chandi
Tole
•Pakistan Bhuka Py...
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.
...
Foundation of COSINE & TANGENT
The origin of terms cosinecosine and tangenttangent was
much later. The cosine function aro...
TRIGONOMETR
IC RATIOS OF
SOME
SPECIFIC
ANGLES
Trigonometric ratios of some
specific angles
Trigonometry ratios of
complimentary angles
Recall two angles are said to be
complimentary if their sum
equals 90°.Sin ( 9...
WHAT ARE
TRIGONOMETRIC IDENTITIES
????
An equation involving
trigonometric ratios of an angle is
called a Trigonometric Id...
Trigonometric identitiesTrigonometric identities
• cos²A + sin²A = 1cos²A + sin²A = 1
• 1 + tan²A = sec²A (1 + tan²A = sec...
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...
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...
ANGLE OF ELEVATION
When a person looks at something above his or her
location, the angle between the line of sight and
the...
ANGLE OF DEPRESSION
When a person looks at something below his or her
location, the angle between the line of sight and
th...
Trigo ppt by mohit manchanda
Trigo ppt by mohit manchanda
Trigo ppt by mohit manchanda
Trigo ppt by mohit manchanda
Trigo ppt by mohit manchanda
Trigo ppt by mohit manchanda
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Trigo ppt by mohit manchanda

  1. 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. 2. Introduction To Trigonometry There is no perhaps nothing which so occupies the middle position of mathematics as trigonometry. -J.F. Herbart(1890)
  3. 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. 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. 5. Trigonometric ratios
  6. 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. 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. 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. 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. 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. 11. TRIGONOMETR IC RATIOS OF SOME SPECIFIC ANGLES
  12. 12. Trigonometric ratios of some specific angles
  13. 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. 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. 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. 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. 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. 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. 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.

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