Question

укажите корень уравнения cosx=-1/2 принадлежащий отрезку -p/2;p/2
а)p/4
b)корней нет
c)p/2
d)p/6

Answer 1

cosx=-1/2
x=+-2Π/3+2Πn, n€Z
Pешим с помощью двойного неравенства:
1) -Π/2<=-2Π/3+2Πn<=Π/2
-Π/2+2Π/3<=2Πn<=Π/2+2Π/3
Π/6<=2Πn<=7Π/6
Π/12<=Πn<=7Π/12
1/12<=n<=7/12
Нет целых чисел.
2) -Π/2<=2Π/3+2Πn<=Π/2
-Π/2-2Π/3<=2Πn<=Π/2-2Π/3
-7Π/6<=2Πn<=-Π/6
-7Π/12<=Πn<=Π/12
-7/12<=n<=1/12
Нет целых чисел.
Ответ: нет корней.