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Primer1:sinx+cosx = we Will construct function graphs of y=sinx u y=1-cosx. (drawing From the schedule it is visible that the equation has 2 decisions: =2π, where p=z and x =π/2+2πk, where kЄZ (It is obligatory to check it calculations). Drawing

With two variables the set of points of the coordinate plane which coordinates turn the equation into right equality is called as the schedule of the equation. Schedules of the equations with two variables are very various. For example, the schedule of the equation 2kh+3u=15 is the straight line, the equations u=5kh2 – 2 – a parabola, the equations h2 +u2=4 – a circle, etc.

The schedule of the first dependence to us is known, it is a parabola; the second dependence - linear; its schedule is a straight line. From the equation (it is visible that rdinata of points of both schedules are equal in that case when x is its decision, among themselves. Means, to this value x there corresponds the same point both on a parabola, and on a straight line, that is the parabola and a straight line are crossed in a point with abtsissy x.

Owing to frequency of the sin x function with the period 2π values x from any integral of a look: (-π/6+2πn; 7π/6 +2πn), nЄZ, are also solutions of an inequality. No other values x solutions of this inequality exist.

On integral (1; + ∞) again we receive a linear inequality 2kh <4, fair at x

If accurately to draw a parabola u=kh2 and a straight line u=2kh-1, we will see that they have one general point (the straight line concerns a parabola, see drawing, h=1, u=1; the equation has one root h=1 (obligatory to check it calculation).

What means to solve the first of these inequalities? It, in essence, means to solve not one inequality, but the whole class, the whole set of inequalities which turn out if to give to parameter and concrete numerical values. The second of the written-out inequalities is a special case of the first as it turns out from it at value and =

Coordinates of any point of the constructed circle are the solution of the equation 1, and coordinates of any point of a parabola are the solution of the equation Means, coordinates of each of points of intersection of a circle and a parabola satisfy both to the first equation of system, and the second, i.e. are the decision of the considered system. Using drawing, we find approximate values of coordinates of points of intersection of schedules: And (-2,2;-4, B(0; C(2,2; 4, D (4;-. Therefore, the system of the equations has four decisions: