Do you need to draw the schedule of trigonometrical function? Master an algorithm of actions on the example of creation of a sinusoid. For the solution of an objective use a research method.
It is required to you
- - ruler;
- - pencil;
- - knowledge of fundamentals of trigonometry.
Instruction
1. Construct y=sin x function graph. A range of definition of this function - a set of all real numbers, area values – an interval [-1; 1]. Means, a sine – function limited. Therefore, on OY axis you will need to note only points with y=-1 value; 0; 1. Draw the system of coordinates and put necessary designations.
2. Periodic y=sin x function. Its period is equal 2π, it is from equality of sin x = sin (x+2π) =sin x for all rational x. At first construct a part of the schedule of the set function on an interval [0; π]. For this purpose it is necessary to find several control points. Calculate schedule points of intersection with OX axis. If y=0, sin x=0, from where x=πk, where k=0; 1. Thus, on this half-cycle the sinusoid crosses OX axis in two points (0; 0) and (π; 0).
3. On an interval [0; π] function a sine accepts only positive values, i.e. the curve lies above OX axis. Function increases from 0 to 1 on a piece [0; π/2] also decreases from 1 to 0 on a piece [π/2; π]. Therefore, on an interval [0; π] the y=sin x function has a maximum point: (π/2; 1).
4. Find some more control points. So, for this function at x=π/6, y=1/2, at x=5π/6, y=1/2. Thus, you have the following points: (0; 0), (π/6; ½), (π/2; 1), (5π/6; ½), (π; 0). Apply them on the coordinate plane and connect a smooth curve. You received y=sin x function graph on an interval [0; π].
5. Now construct the schedule of this function for a negative half-cycle [-π; 0]. For this purpose execute symmetry of the received schedule to the beginning of coordinates. It allows to make oddness of the y=sin x function. You received y=sin x function graph on an interval [-π; π].
6. Using frequency of the y=sin x function, you can continue a sinusoid on OX axis without finding of control points to the right and to the left. You received y=sin x function graph on all numerical straight line.