“A mathematician knows how to solve a problem, he can’t solve
it.” ~MILNE
INTROUDUCTION TO TRIGONOMETRY (TRIGONOMETRIC functions)
The
word trigonometry was derived from greek words TRIGONO means
TRIANGLES
METRY mean
MEASURES
The
word trigonometry literally means “the measurement of angles of a triangle”.
HISTORY OF TRIGONOMETRY
·
The
study of trigonometry was first started in india.
·
The
ancent indian aryabhatta, brahmagupta, bhaskara 1 and bhaskara 2 got important
result.
·
All
this knowledge first went from india to middle-east and from there to Europe
·
In
india, the predecessor of the modern trigonometric functions, known as the sine of an ange
·
The
main contribution of the siddhantas
BHASKARA 1(600) & BHASKARA 2(1114)
·
He
gave formula to find the values of sine functions for an angle more than 900
·
A
sixth century Malayalam work yuktibhasa contains a proof for the
expansion of sin(A+B)
THE SYMBOLS sin-1 x, cos-1x, etc., for
arc sin x , cos x, etc., were
suggested by the astronomer sir john F.W.hersehel(1813)
Applications
Used in the navigation (sea captains),
surveyor
Used in seismology, design electric
circuits, state of an atom, predicting the height of tides in the ocean, etc.
For ex: Determination of the
height of a great
Pyramid in Egypt by measuring shadows
Of the pyramid
(H/S)=(h/s)=tan(sun’s altitude)
SOME BASICS ON
TRIGONOMETRY
ANGLES
DEGREE MEASUR
RADIAN MEASURE
ANGLES
An angle consists of two rays with a common End-point (or, initial point). Each ray is a side of the angle.
The common endpoint is called the vertex of the Angle.
Degree
The symbol for degrees is ⁰ INITIAL TO TERMINAL SIDE is (1/360 )th of
revolutions.
RADIAN
Circumference of circle is called
radians
