Available online
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.
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 |
|---|---|
| Item code: | MS283; 03 |
| First transmission date: | 14-03-1979 |
| Published: | 1979 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:20 |
| + Show more... | |
| Producer: | David Saunders |
| Contributors: | Norman Gowar; Bob Margolis |
| Publisher: | BBC Open University |
| Keyword(s): | Rotation; Transformation; Translation; Sine; Cosine |
| Footage description: | 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. |
| Master spool number: | 6HT/73034 |
| Production number: | 00525_4312 |
| Videofinder number: | 482 |
| Available to public: | no |
