To solve the inequality sin(x-π/4) ≤ -1, we first need to find the values of x that satisfy the inequality.
Since the range of the sine function is between -1 and 1, sin(x-π/4) can only be less than or equal to -1 when sin(x-π/4) = -1.
So, we need to find the values of x that make sin(x-π/4) = -1. This occurs when x - π/4 = -π/2 + 2πn, where n is an integer.
Solving for x, we get x = -π/4 - π/2 + 2πn = -3π/4 + 2πn.
Therefore, the solution to the inequality sin(x-π/4) ≤ -1 is x ≤ -3π/4 + 2πn, where n is an integer.
To solve the inequality sin(x-π/4) ≤ -1, we first need to find the values of x that satisfy the inequality.
Since the range of the sine function is between -1 and 1, sin(x-π/4) can only be less than or equal to -1 when sin(x-π/4) = -1.
So, we need to find the values of x that make sin(x-π/4) = -1. This occurs when x - π/4 = -π/2 + 2πn, where n is an integer.
Solving for x, we get x = -π/4 - π/2 + 2πn = -3π/4 + 2πn.
Therefore, the solution to the inequality sin(x-π/4) ≤ -1 is x ≤ -3π/4 + 2πn, where n is an integer.