To solve the equation cos(x + π/3) = -1 in the interval [-2π, π/2], we first need to find the values of x that satisfy this equation.
Since the cosine function has a period of 2π, we can simplify the interval to just [0, 2π]. The general solution for cos(x) = -1 is x = π + 2πn, where n is an integer.
Now, we need to consider the angle inside the cosine function: (x + π/3). When the cosine of an angle is -1, the angle must be π, so we have:
x + π/3 = π
Solving for x, we get x = π - π/ x = 2π/3
Since 2π/3 is between 0 and 2π, it satisfies the given interval.
Therefore, the solution to the equation cos(x + π/3) = -1 in the interval [-2π, π/2] is x = 2π/3
To solve the equation cos(x + π/3) = -1 in the interval [-2π, π/2], we first need to find the values of x that satisfy this equation.
Since the cosine function has a period of 2π, we can simplify the interval to just [0, 2π]. The general solution for cos(x) = -1 is x = π + 2πn, where n is an integer.
Now, we need to consider the angle inside the cosine function: (x + π/3). When the cosine of an angle is -1, the angle must be π, so we have:
x + π/3 = π
Solving for x, we get
x = π - π/
x = 2π/3
Since 2π/3 is between 0 and 2π, it satisfies the given interval.
Therefore, the solution to the equation cos(x + π/3) = -1 in the interval [-2π, π/2] is
x = 2π/3