Solution to problem 7.1.8 from the collection of Kepe O.E.

Solution to problem 7.1.8 from the collection of Kepe O.?.

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Our product is an electronic version of the solution to problem 7.1.8, which contains a detailed description and step-by-step solution to the problem. The solution is presented in the form of a beautiful HTML document that is easy to read and understand.

Solution to problem 7.1.8 from the collection of Kepe O.?. is an educational material for students and schoolchildren studying mathematics and physics. This problem is an example of the use of trigonometric functions and vector algebra in solving problems on the plane.

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Our digital goods store invites you to purchase the solution to problem 7.1.8 from the collection of Kepe O.?. This is an electronic version of the solution to the problem, which contains a detailed description and step-by-step solution, formatted in a beautiful HTML document. The solution to the problem is intended for students and schoolchildren studying mathematics and physics. It will help them better understand the material and successfully solve problems on the plane, using knowledge from the field of trigonometric functions and vector algebra. By purchasing our product, you get access to complete and understandable information that will help you increase your level of knowledge in these subjects. Don't miss the opportunity to purchase our product today and improve your knowledge in mathematics and physics!

We suggest you purchase an electronic version of the solution to problem 7.1.8 from the collection of Kepe O.?. The solution contains a detailed description and step-by-step solution to the problem, formatted in a beautiful HTML document.

The task is to determine the nearest moment in time when the radius vector of a point moving according to the equations x = sin t, y = cos t forms an angle of 45° with the Ox axis. To solve the problem, it is necessary to use knowledge from the field of trigonometric functions and vector algebra.

Our solution is intended for students and schoolchildren studying mathematics and physics, and will help them better understand the material and successfully solve problems on a plane. By purchasing our product, you get access to complete and understandable information that will help you increase your level of knowledge in these subjects.

Don't miss the opportunity to purchase our solution today and successfully solve problem 7.1.8 from the collection of Kepe O.?. The answer to the problem is 0.785.

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Solution to problem 7.1.8 from the collection of Kepe O.?. consists in determining the nearest moment in time when the radius vector of a point, drawn from the origin, forms an angle of 45 degrees with the Ox axis.

To solve the problem, it is necessary to express the radius vector of a point through the equations of motion, then substitute the resulting expressions into the equation for the angle between the radius vector and the Ox axis. After this, you should find the derivative of the angle and equate it to zero in order to determine the moment in time at which the radius vector forms an angle of 45 degrees with the Ox axis.

Specifically in this problem, the radius vector of a point has the form r = (x^2 + y^2)^0.5 = (sin^2(t) + cos^2(t))^0.5 = 1. The expression for the angle between the radius -vector and axis Ox can be found using the following formula:

cos(α) = x/r = sin(t)/r

where α is the angle between the radius vector and the Ox axis.

From the conditions of the problem it follows that cos(α) = cos(45 degrees) = √2/2. Substituting the expressions for x and r into this formula, we get:

√2/2 = sin(t)

Where do we find t:

t = arcsin(√2/2) = π/4 = 0,785

Thus, the closest moment in time when the radius vector of a point forms an angle of 45 degrees with the Ox axis is 0.785.

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