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The first quarter of the trigonometrical circumference

Visual didactic materials
źThe first quarter of the trigonometrical circumference╗

           The series źThe first quarter of the trigonometrical circumference╗ of the collection źThe trigonometrical circumference╗
is aimed to form primary ideas of the most important trigonometrical concepts.
           The main aim is for pupils to see what źremarkable numbers╗ they can see, how and where, going to construction and visual determination of correlation of sines and cosines of the remarkable angles to these numbers then; for them to find out what part the źremarkable points╗ play in constructionof the graph of function onto the interval from 0 to ¤/2.

           These films can be reproduced on any computer having WINDOWS version 95 (and higher versions) without an additional installation of special programmes as they are made in EXE format.

           The principle of operation: the changing of frames is executed by pushing of a printed(graphical) button. Movement is is possible both “forward” and “backward”.

           Slide-films are meant for group study and can be used by a teacher at school lessons spontaneity.The principle of operation the film offering by us gives an opportunity to stop at the frames demanding special attention.

The first quarter of the trigonometrical circumference

1. The remarkable angles of the first quarter of the trigonometrical circumference
2. The remarkable radicals on the radiuses of the first quarter of the trigonometrical circumferen˝e
3. The remarkable sines and cosines of the angles of the first quarter of the trigonometrical circumference
4. The radian measure of the remarkable angles of the first quarter of the trigonometrical circumference
5. The remarkable radians and numbers of the first quarter of the trigonometrical circumference
6. The graph of sine in the interval from 0 to ¤/2 on the plotted paper
7. The graph of cosine in the interval from 0 to ¤/2 on the plotted paper
Brief contents of the series
 

╣1. The remarkable angles of the first quarter of the trigonometrical circumference

Frame from the film

      

       The film shows how to construct remarkable angles rather exactly without a protractoron by means of a pen and a pair of compasses on plotted paper .

       Itĺs useful to pay attention of students to comfortable for calculations and corresponding constructions significances of the remarkable angles, for which angles of 0, 30, 45, 60 and 90 degrees of the first quarter of the trigonometrical circumference are taken.

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╣2. The remarkable radicals on the radiuses of the first quarter of the trigonometrical circumferen˝e

Frame from the film

       The film shows how to mark some special numbers which are called the remarkable radicals on the radiuses of the trigonometricalcircumferen˝e there rather precise on plotted paper.

       Itĺs useful to pay attention of students to comfortable for calculations and corresponding constructions significances of the remarkable radicals, which are the coordinates of the points forming on the first quarter of the trigonometrical circumference.

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╣3. The remarkable sines and cosines of the angles of the first quarter of the trigonometrical circumference
Frame from the film

       The film shows how to determine the significances of sines and cosines of the remarkable angles on the base of already learnt ways

       The connection of the remarkable angles of the first quarter of the trigonometrical circumference and corresponding remarkable sines and cosines as which sines and cosines of the remarkable angles are implied should be paid attention of students to.

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╣4. The radian measure of the remarkable angles of the first quarter of the trigonometrical circumference

Frame from the film

       The film shows how to mark sines and cosines of the remarkable angles of the first quarter of the trigonometrical circumference expressed in radians on the line of sines and cosines. Besides,the comparison of equal significances of remarkable sines and cosines for different angles takes place.

       The way the radian and the degree measures of the remarkable angles are connected should be paid attention to.

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╣5. The remarkable radians and numbers of the first quarter of the trigonometrical circumference

Frame from the film

       The film shows how to determine rather exactly the position of the remarkable radians and radicals on the axis of special trigonometrical system of coordinates hith help of of the models of the first quarter of the trigonometrical circumferen˝e there on plotted paper.

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╣6. The graph of sine in the interval from 0 to ¤/2 on the plotted paper

Frame from the film

       The film shows how to construct the graph of sines and cosines in the interval from 0 to ¤/2 with help of the remarkable points of the first quarter of the trigonometrical circumferen˝e on plotted paper.

       The students are supposed to be given the basic ideas of construction of the graph of sines in the trigonometrical co-ordinate system, which is determined as a curve passing through the remarkable points of the sine.

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╣7. The graph of cosine in the interval from 0 to ¤/2 on the plotted paper

Frame from the film

       The film shows that construction of the remarkable cosines on plotted paper also takes place on the axis of significance of the trigonometrical function.The remarkable radians are also laid of the first quarter of the trigonometrical circumferen˝e on the axis of its argument.

       The students are supposed to be given the basic ideas of peculiarities of construction of the graph of cosines in the trigonometrical system of coordinates, which is also determined as a curve passing through its remarkable points .

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The authorĺs group:
Conception and visualisation - Reznik N.A.
Planning and visual organisation - Yezhova N.M.
Selection of lexical material,approving and adaptation - Karasev A.A.
Mathematical editing and ˛esting - Temnikova I.S.
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The first quarter of the trigonometrical circumferen˝e

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ę Natalya Reznik (nareznik@yandex.ru): the chief of the project “The visual school”
ę Natalia Yezhova (naegova@yandex.ru): the methodologist-elaborator of the web site
ę Aleksey Baryshkin: design the mock-up of the web site
ę Anrey Karasev: translator

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