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Description
The programme aims to derive a proof for the formula expressing sin (alpha + beta) as cos alpha sin beta + sin alpha cos beta and to show how transformations of the plane can be employed to obtain ...this result.
Module code and title: MS283, An introduction to calculus MS283; 03 14-03-1979 1979 Rights owned or controlled by The Open University This material can be used in accordance with The Open University conditions of use. A link to the conditions can be found at the bottom of all OU Digital Archive web pages. 00:24:20 + Show more... David Saunders Norman Gowar; Bob Margolis BBC Open University Rotation; Transformation; Translation; Sine; Cosine Norman Gowar briefly sums up ways of expressing sines of angles in standard triangles. He goes on to point out the desirability of finding a formula which would allow the expression of sines and cosines of angles of non-standard triangles. Gowar goes on to explain that the key to obtaining this formula is to regard the angles as angles of rotation in a plane. Bob Margolis approaches the problem of rotation in a plane by first demonstrating the translation of points in a plane. He manipulates shapes on a board and shows an animation as he talks. Margolis arrives at a general formula for expressing the translation of a point in a plane. Margolis, with the aid of animations, tries without success to use the formula above for describing the rotation of points in a plane. Norman Gowar sums up the programme so far and sets out what still needs to be done in order to obtain a general formula for the rotation of angles in a plane. Margolis, with the aid of several animated diagrams and a graphics board, derives a rule which explains where a general poirot u, v goes when rotated through an angle alpha. Gorman Gowar sums up the programme so far and goes on to work out a formula (...) and test it. Gowar sums up the programme. A series of trigonometric formulae are captioned as he talks. 6HT/73034 00525_4312 482 no