**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 |
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Item code: | MS283; 03 |

First transmission date: | 14-03-1979 |

Published: | 1979 |

Rights Statement: | Rights owned or controlled by The Open University |

Restrictions on use: | 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. |

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 |