Use of trigonometric functions in operating Canadarm2
The Canadarm2 robotic manipulator on the International Space Station is operated by controlling the angles of its joints. Calculating the final position of the astronaut at the end of the arm requires repeated use of trigonometric functions of those angles.
The word 'Trigonometry' is derived from the Greek roots "tri", "gonia", "metron". Here "Tri" means 'three', "Gonia" means 'an angle', "Metron" means 'measure'. So 'trigonometry' means "the measurement of three angles". It is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. 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.
The origins of trigonometry can be traced to the civilizations of ancient Egypt, Mesopotamia and the Indus valley (India), more than 4000 years ago. The common practice of measuring angles in degrees, minutes and seconds comes from the Babylonian's base sixty system of numeration.
The Indian mathematician Aryabhatta gave tables of half chords which are now known as sine tables, along with cosine tables. He used zya for sine, kotizya for cosine and otkram zya for inverse sine. Another Indian mathematician, Brahmagupta used an interpolation formula to compute values of sines.