Question

Выведите формулы , выражающие координаты точки А с неотрицательной ординатой через длину отрезка ОА и угол между лучом ОА и положительной полуосью Ох

Answer 1

Ответ:

Если длина отрезка OA = l, а угол между лучом OA и положительной полуосью Ox равен α, то координаты точки A определяются по формулам: Ax = l·cosα и Ay = l·sinα.

Объяснение:

Вывод формул в приложении.

Answer 2

I will answer in detail. To derive the formulas that express the coordinates of point A with a non-negative ordinate through the length of segment OA and the angle between ray OA and the positive x-axis, we can use the following steps:

- Let O be the origin of the coordinate system, and let a be the angle between ray OA and the positive x-axis. - Draw a perpendicular line from point A to the x-axis, and let B be the point of intersection. - Then, triangle OAB is a right triangle, and we can use trigonometric ratios to find the coordinates of point A. - The length of segment OB is the abscissa of point A, denoted by x. The length of segment AB is the ordinate of point A, denoted by y. The length of segment OA is denoted by r. - By definition, cos(a) = x/r and sin(a) = y/r. Solving for x and y, we get x = r*cos(a) and y = r*sin(a). - These are the formulas that express the coordinates of point A through r and a.

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