NIKHIL V. NAIR DISHA MADAANISHA MEHRA RIDHIMA ARORA ZUBIN MALOTHRAAKSHIT JAINUMANG MISHRA

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.

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.

Basic identities:-

Q) tan x sin x + cos x = sec xSolution: 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

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

APPLICATIONS OF TRIGONOMETRY

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.

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.

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.

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