### COURSE REVIEWS

COURSE DETAILS

**Trigonometry** (from Greek *trigōnon*, "triangle" and *metron*, "measure"^{[1]}) is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.^{[2]}

The 3rd-century astronomers first noted that the lengths of the sides of a right-angle triangle and the angles between those sides have fixed relationships: that is, if at least the length of one side and the value of one angle is known, then all other angles and lengths can be determined algorithmically. These calculations soon came to be defined as the trigonometric functions and today are pervasive in both pure and applied mathematics: fundamental methods of analysis such as the Fourier transform, for example, or the wave equation, use trigonometric functions to understand cyclical phenomena across many applications in fields as diverse as physics, mechanical and electrical engineering, music and acoustics, astronomy, ecology, and biology. Trigonometry is also the foundation of surveying.

Trigonometry is most simply associated with planar right-angle triangles (each of which is a two-dimensional triangle with one angle equal to 90 degrees). The applicability to non-right-angle triangles exists, but, since any non-right-angle triangle (on a flat plane) can be bisected to create two right-angle triangles, most problems can be reduced to calculations on right-angle triangles. Thus the majority of applications relate to right-angle triangles. One exception to this is spherical trigonometry, the study of triangles on spheres, surfaces of constant positive curvature, in elliptic geometry (a fundamental part of astronomy and navigation). Trigonometry on surfaces of negative curvature is part of hyperbolic geometry.

#### Chapter 1: Trigonometry

- 1379 slides
- 2535 slides
- 310 slides
- 4200 slides
- 5
Lecture 5: Prakash Gorroochurn

328 slides - 6538 slides
- 7475 slides
- 8
Lecture 8: Harry Schwarzlander

623 slides - 9633 slides
- 10157 slides
- 11440 slides
- 12320 slides
- 13
Lecture 13: Burnside, William,

14 slides - 14673 slides
- 154 slides
- 16300 slides
- 17200 slides
- 18725 slides
- 19722 slides
- 20705 slides
- 21213 slides
- 22335 slides
- 231117 slides
- 24224 slides
- 25338 slides
- 268 slides
- 27416 slides
- 28229 slides
- 29241 slides
- 30911 slides
- 31
Lecture 31: Nittis Mukhopadhyay

690 slides - 32
Lecture 32: Richard N. Aufmann

1076 slides - 33408 slides
- 341442 slides
- 35
Lecture 35: Douglas C. Montgomery

836 slides - 36
Lecture 36: E. E. Bassett et al.

240 slides