Trigonometry is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. It defines trigonometric functions that describe these relationships and are applicable to cyclical phenomena like waves. Trigonometry has its origins in ancient Greek and Indian mathematics and was further developed by Islamic mathematicians. It is the foundation of surveying and has many applications in fields like astronomy, music, acoustics, and more.

1. TRIGONOMETRY
MADE BY:- PRINCE
GOYAL
NIMIT ARORA

2. TRIGONOMETRY
Trigonometry (from Greek trigōnon "triangle"
+ metron "measure") is a branch of mathematics that
studies triangles and the relationships between the
lengths of their sides and the angles between those
sides.

3. Trigonometry defines the trigonometric
functions, which describe those
relationships and have applicability
to cyclical phenomena, such as waves.
The field evolved during the third
century BC as a branch
of geometry used extensively for
astronomical studies . It is also the
foundation of the practical art
of surveying.

4. HISTORY Of TRIGONOMETRY
Classical Greek
mathematicians (such
as Euclid and Archimed
es) studied the
properties
of chords and inscribed
angles in circles, and
proved theorems that
are equivalent to
modern trigonometric
formulae, although they
presented them
geometrically rather
than algebraically.

5. The modern sine
function was first
defined in the Surya
Siddhanta, and its
properties were
further documented
by the 5th
century Indian
mathematician and
astronomer Aryabh
ata.

6. These Greek and Indian works were translated
and expanded by medieval Islamic
mathematicians. By the 10th century, Islamic
mathematicians were using all six
trigonometric functions, had tabulated their
values, and were applying them to problems
in spherical geometry.

7. The Father of Trigonometry
The
first trigonometri
c table was
apparently
compiled
by Hipparchus,
who is now
consequently
known as "the
father of

8. RIGHT TRIANGLE
A right triangle or right-
angled triangle is
a triangle in which
one angle is a right
angle (that is, a 90-
degree angle). The
relation between the
sides and angles of a
right triangle is the
basis for trigonometry.

9. The side opposite the right
angle is called
the hypotenuse (side c in
the figure above). The
sides adjacent to the right
angle are called legs.
Side a may be identified as
the side adjacent to angle
B and opposed
to (or opposite) angle A,
while side b is the
side adjacent to angle
A and opposed to angle B.

10. PYTHAGORAS THEOREM
The Pythagorean theorem:
The sum of the areas of the
two squares on the legs (a
and b) equals the area of the
square on the hypotenuse
(c).

11. If one angle of a triangle is 90 degrees
and one of the other angles is known, the
third is thereby fixed, because the three
angles of any triangle add up to 180
degrees. The two acute angles therefore
add up to 90 degrees: they
are complementary angles. The shape of
a triangle is completely determined,
except for similarity, by the angles.
TRIGONOMETRIC RATIOS

12. Once the angles are known,
the ratios of the sides are
determined, regardless of the
overall size of the triangle. If the
length of one of the sides is
known, the other two are
determined. These ratios are given
by the following trigonometric
functions of the known angle A,
where a, b and c refer to the
lengths of the sides in the

14. The hypotenuse is the side opposite to the 90 degree angle in a
right triangle; it is the longest side of the triangle, and one of the
two sides adjacent to angle A. The adjacent leg is the other side
that is adjacent to angle A. The opposite side is the side that is
opposite to angle A. The terms perpendicular and base are
sometimes used for the opposite and adjacent sides respectively.
The reciprocals of these functions are named the cosecant (csc or
cosec), secant (sec), and cotangent (cot), respectively:

15. TRIGONOMETRIC FUNCTIONS

16. STANDARD IDENTITIES
Identities are those equations that hold true for any value

17. REDUCTION FORMULA
Sin (90-A) =Cos A
Tan (90-A)= Cot
A
Cosec (90-A)= Sec
A

18. Calculator1) This calculates the value of
trigonometric functions of
different angles.
2) First enter whether you
want enter the angle in
radian or in degree.
3) Then enter the required
trigonometric function in
the format given below:
4) Enter 1 for Sin
5) Enter 2 for Cosine
6) Enter 3 for tangent
7) Enter 4 for Cosecant
8) Enter 5 for Secant
9) Enter 6 for cotangent
10)Then enter the magnitude
of angle.

19. Applications of trigonometry
Fields that use trigonometry or trigonometric functions
include astronomy (especially for locating apparent positions of
celestial objects, in which spherical trigonometry is essential)
and hence navigation (on the oceans, in aircraft, and in
space), music theory, audio synthesis, acoustics, optics,
analysis of financial markets, electronics, probability
theory, statistics, biology, medical imaging (CAT
scans and ultrasound)

20. Application of trigonometry in
Astronomy
1) Since ancient times trigonometry was used in
astronomy
2) The technique triangulation is used to measure the to
nearby stars .
3) In 240 B.C, a mathematician named Eratosthenes
discovered the radius of the earth using trigonometry
and geometry
4) In 2001 , a group of European astronomers did an
experiment that started in 1997 about the distance of
Venus from the sun.

21. conclusion
TRIGONOMETRY IS A BRANCH OF
MATHEMATICS WITH SEVERAL
IMPORTANT AND USEFUL
APPLICATIONS.HENCE IT
ATTRACTSMORE AND MORE
RESEARCHWITH SEVERAL THEORIES
PUBLISHED YEAR AFTER YEAR.
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