Question

Найти абсциссы тех точек графика функции y=sinX*cosX, ординаты которых равны 0,25

Answer 1

Я не уверен но,Y=sinx*cosx окружность.Ордината соответственно Это ось OY,то есть нам необходимо найти значения Sinx=0,25,А это П/4 При П/4 Абсцисса и ордината равны,значит Ордината тоже будет равна 0,25 

Answer 2

Finding Abscissas of Points on the Graph of y=sin(x)*cos(x) with Ordinates 0.25

To find the abscissas of the points on the graph of the function y=sin(x)*cos(x) with ordinates equal to 0.25, we can use the trigonometric identity sin(2x) = 2sin(x)cos(x) to simplify the given function.

The function y=sin(x)*cos(x) can be rewritten as y = 0.5sin(2x) using the double angle identity for sine.

Now, to find the abscissas of the points on the graph where the ordinates are 0.25, we can solve the equation 0.5sin(2x) = 0.25 for x.

Using the given information, we can solve for x as follows:

0.5sin(2x) = 0.25

sin(2x) = 0.5

Now, we need to find the values of x that satisfy the equation sin(2x) = 0.5.

Solution:

The solutions for the equation sin(2x) = 0.5 can be found using inverse trigonometric functions. The solutions will be the values of x that satisfy the equation.

Using the inverse sine function, we can find the values of 2x:

2x = arcsin(0.5) + 2πn or 2x = π - arcsin(0.5) + 2πn

Where n is an integer.

Solving for x, we get:

x = (arcsin(0.5) + 2πn) / 2 or x = (π - arcsin(0.5) + 2πn) / 2

Now, we can calculate the values of x using the above equations.

Calculated Abscissas:

The calculated abscissas of the points on the graph of the function y=sin(x)*cos(x) with ordinates equal to 0.25 are:

x = (arcsin(0.5)) / 2 ≈ 0.5236 + πn or x = (π - arcsin(0.5)) / 2 ≈ 1.0472 + πn

where n is an integer.

These are the values of x that correspond to the points on the graph where the ordinates are 0.25.