Trigo ppt by mohit manchanda
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Transcript of Trigo ppt by mohit manchanda
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.
Introduction
Introduction To Trigonometry
There is no perhaps nothing which so occupies the middle position of mathematics as trigonometry.
-J.F. Herbart(1890)
•Suppose the students of a
school are
visiting Qutub Minar. N
ow, if a student
is looking at the to
p of the Minar a
right tr
iangle could be imagined to
be
made.
• Suppose a girl sitti
ng on the
balcony of her h
ouse located on
the bank of a riv
er. She is looking
down at a flower p
ot placed on
stair of a
temple situ
ated nearby
on the other b
ank of the riv
er. A
right tr
iangle is imagined to
be
made in th
is situatio
n.
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
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 ABC
A B
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
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
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
SinSin
Sin
Sin
Sin
Sin
Sin
Sin
Sin
Sin
SinSin
Sin
ORIGIN OF ‘SINE’
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.
TRIGONOMETRIC 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 ( 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.
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 relationships between certain trigonometric functions.
Trigonometric Trigonometric identitiesidentities
• 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 ≤ 0* < A ≤ 90*)90*)
OTHER USEFUL IDENTITIES
• Sin θ = 1/cosec θ• Cos θ = 1/sec θ• Tan θ = 1/cot θ• Cosec θ = 1/sin θ• Sec θ = 1/cos θ• Tan θ = 1/cot θ
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
ANGLE OF ELEVATIONWhen 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.
ANGLE OF DEPRESSIONWhen 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.