Помогите решить уравнение для графика y = 1/2 cos x - 3. Каковы значения функции y для следующих углов?

1. y(0) = 1/2 cos 0 - 3 =
2. y(π/6) = 1/2 cos π/6 - 3 =
3. y(π/3) = 1/2 cos π/3 - 3 =
4. y(π/2) = 1/2 cos π/2 - 3 =
5. y(2π/3) = 1/2 cos 2π/3 - 3 =
6. y(5π/6) = 1/2 cos 5π/6 - 3 =
7. y(π) = 1/2 cos π - 3 =
8. y(7π/6) = 1/2 cos 7π/6 - 3 =
9. y(4π/3) = 1/2 cos 4π/3 - 3 =
10. y(3π/2) = 1/2 cos 3π/2 - 3 =
11. y(5π/3) = 1/2 cos 5π/3 - 3 =
12. y(11π/6) = 1/2 cos 11π/6 - 3 =
13. y(2π) = 1/2 cos 2π - 3 =

Математика 11 класс Графики функций уравнение графика значения функции y cos x математика решение уравнения Углы Тригонометрия график функции Новый

Давайте решим уравнение y = 1/2 cos x - 3 для заданных углов. Мы будем подставлять значения x и вычислять соответствующие значения y.

Формула для вычисления y выглядит следующим образом:

y(x) = 1/2 * cos(x) - 3

Теперь подставим значения x:

• y(0):
  • cos(0) = 1
  • y(0) = 1/2 * 1 - 3 = 1/2 - 3 = -5/2 = -2.5
• y(π/6):
  • cos(π/6) = √3/2
  • y(π/6) = 1/2 * (√3/2) - 3 = √3/4 - 3
• y(π/3):
  • cos(π/3) = 1/2
  • y(π/3) = 1/2 * (1/2) - 3 = 1/4 - 3 = -11/4 = -2.75
• y(π/2):
  • cos(π/2) = 0
  • y(π/2) = 1/2 * 0 - 3 = 0 - 3 = -3
• y(2π/3):
  • cos(2π/3) = -1/2
  • y(2π/3) = 1/2 * (-1/2) - 3 = -1/4 - 3 = -13/4 = -3.25
• y(5π/6):
  • cos(5π/6) = -√3/2
  • y(5π/6) = 1/2 * (-√3/2) - 3 = -√3/4 - 3
• y(π):
  • cos(π) = -1
  • y(π) = 1/2 * (-1) - 3 = -1/2 - 3 = -7/2 = -3.5
• y(7π/6):
  • cos(7π/6) = -√3/2
  • y(7π/6) = 1/2 * (-√3/2) - 3 = -√3/4 - 3
• y(4π/3):
  • cos(4π/3) = -1/2
  • y(4π/3) = 1/2 * (-1/2) - 3 = -1/4 - 3 = -13/4 = -3.25
• y(3π/2):
  • cos(3π/2) = 0
  • y(3π/2) = 1/2 * 0 - 3 = 0 - 3 = -3
• y(5π/3):
  • cos(5π/3) = 1/2
  • y(5π/3) = 1/2 * (1/2) - 3 = 1/4 - 3 = -11/4 = -2.75
• y(11π/6):
  • cos(11π/6) = √3/2
  • y(11π/6) = 1/2 * (√3/2) - 3 = √3/4 - 3
• y(2π):
  • cos(2π) = 1
  • y(2π) = 1/2 * 1 - 3 = 1/2 - 3 = -5/2 = -2.5

Теперь у нас есть значения функции y для всех указанных углов:

• y(0) = -2.5
• y(π/6) = √3/4 - 3
• y(π/3) = -2.75
• y(π/2) = -3
• y(2π/3) = -13/4
• y(5π/6) = -√3/4 - 3
• y(π) = -3.5
• y(7π/6) = -√3/4 - 3
• y(4π/3) = -13/4
• y(3π/2) = -3
• y(5π/3) = -2.75
• y(11π/6) = √3/4 - 3
• y(2π) = -2.5