Question

Y=cosx; y=0; x=0; x=п/2

Answer 1

Площадь фигуры S образованной заданными линиями, будет равна интегралу:

S = ∫cos(x) * dx|0;π/2 = (-sin(x))|0;π/2 = sin(π/2) - (-sin(0)) = 1 + 0 = 1.

Ответ: искомая площадь, образованная функцией y = cos(x) и осью абсцисс на интервале от 0 до π/2 равна 1.

Answer 2

To find the values of x where y = cos(x) equals zero, we can set y to zero and solve for x.

Given: y = cos(x) y = 0

Substituting y with 0, we have: 0 = cos(x)

To find the values of x that satisfy this equation, we can refer to the unit circle or use the trigonometric identity cos(x) = 0 at certain angles.

The cosine function is equal to zero at x = π/2 and x = 3π/2 (or x = 90° and x = 270° in degrees). These angles correspond to the points where the unit circle intersects the x-axis.

Therefore, the solutions for x in the equation y = cos(x) when y = 0 are: x = π/2 (or x = 90°) x = 3π/2 (or x = 270°)