Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. It emerged during the 3rd century BC from applications of geometry to astronomy. Hipparchus is considered the founder of trigonometry, compiling the first trigonometric table in the 2nd century BC. Key trigonometric functions like sine, cosine, and tangent were discovered between the 5th-10th centuries CE by mathematicians including Aryabhata, Muhammad ibn Musa al-Khwarizmi, and Abu al-Wafa. Trigonometry is applied to calculate angles of elevation and depression used in applications like determining the angle an airplane is viewed from the ground.

3. NIKHIL V. NAIR
DISHA MADAAN
ISHA MEHRA
RIDHIMA ARORA
ZUBIN MALOTHRA
AKSHIT JAIN
UMANG MISHRA

4.  Trigonometry (from Greek trigōnon,
"triangle" and metron, "measure") is a branch
of mathematics that studies relationships
involving lengths and angles of triangles. The
field emerged during the 3rd century BC from
applications of geometry to astronomical
studies.

5. It is the Greek astronomer and mathematician HipparcHus of Nicaea
in Bithynia (190 BCE - 120 BCE) that is often considered as the founder
of the science of trigonometry. According to the Greek scholar THeon
of alexandria (335 CE – 405 CE), Hipparchus compiled a “table
of chords” in a circle (a trigonometric table) in 12 books.
Regarding the six trigonometric functions: aryabHaTa (476 CE -
550 CE) discovered the sine and cosine; MuHaMMad ibn Musa
al-KHwariziMi (780 CE - 850 CE) discovered the tangent; abu
al-wafa’ buzjani (940 CE - 988 CE) discovered the secant,
cotangent, and cosecant.
alberT Girard (1595-1632), a French mathematician, was the
first to use the abbreviations sin, cos, and tan in a treatise.

9.  Basic identities:-

11. Q) tan x sin x + cos x = sec x
Solution: We will only use the fact that sin² x +
cos² x = 1 for all values of x.
LHS = tan x sin x + cos x
=>sin x/cos x. sin x +cosx
= >sin² x/ cos x + cos x
=>sin² x/ cos x + cos²x /cosx
=> sin² x + cos² x/ cos x
= >1/ cos x = RHS

13. Q) Cos² 20+cos² 70/sin² 31+sin² 59+sin²
64+cos64.sin26
Solution:- cos² 20+sin² (90-70)/sin² 31+sin² (90-
59)+sin² 64+cos64.cos64
=> 1+sin² 64+cos² 64
=>1+1
=>2

14. APPLICATIONS OF
TRIGONOMETRY

15.  We observe generally that children usually
look up to see an airplane when it passes
overhead. This line joining their eye to the
plane while looking up is called LINE OF
SIGhT.

16.  The angle which the line of sight makes with a
horizontal line drawn away from their eyes is
called the angle of elevation of airplane
from them.

17.  If the pilot of the airplane looks downward at
any object on the ground then the angle
between his line of sight and horizontal line
drawn away from his eyes is called angle of
depression.

20.  NIKHIL V. NAIR
 DISHA MADAAN
 ISHA MEHRA
 RIDHIMA ARORA
 AKSHIT JAIN
 ZUBIN MALOTHRA
 UMANG MISHRA