Question

найдите абциссы общих точек графиков функции y=sinx и y=sin2x

Answer 1

общие точки когда sin2x=sinx

sin2x-sinx=0

2sinxcosx-sinx=0

sinx(2cosx-1)=0

sinx=0или cos x=0,5

x=πk,k∈Z или x=±π/3+2πn,n∈Z

Answer 2

Finding the Common Points of the Graphs of y = sin(x) and y = sin(2x)

To find the abscissas of the common points of the graphs of the functions y = sin(x) and y = sin(2x), we can set the two functions equal to each other and solve for x.

The general form of the sine function is y = A sin(Bx + C), where A is the amplitude, B is the frequency, and C is the phase shift. For y = sin(x), A = 1, B = 1, and C = 0. For y = sin(2x), A = 1, B = 2, and C = 0.

Setting y = sin(x) equal to y = sin(2x) gives us the equation sin(x) = sin(2x).

To find the common abscissas, we can use the trigonometric identity sin(A) = sin(B) if and only if A = nπ + (-1)^n * B, where n is an integer.

By applying this identity to sin(x) = sin(2x), we get x = nπ + (-1)^n * 2x.

Solving for x, we get x = nπ, where n is an integer.

Therefore, the common abscissas of the graphs of y = sin(x) and y = sin(2x) are x = nπ, where n is an integer.

This means that the common points occur at every integer multiple of π.