To solve the equation cos(x) = -1/√2, we need to determine the values of x that satisfy this equation.
Since the cosine function is negative in the second and third quadrants, we can find the reference angle whose cosine is 1/√2 and then find the corresponding angles in those quadrants.
The reference angle whose cosine is 1/√2 is π/4 (45 degrees).
In the second quadrant, the angle whose cosine is -1/√2 is π - π/4 = 3π/4 (135 degrees).
In the third quadrant, the angle whose cosine is -1/√2 is 2π - π/4 = 7π/4 (315 degrees).
Therefore, the solutions to the equation cos(x) = -1/√2 are:
x = 3π/4 + 2πn, where n is an integer x = 7π/4 + 2πn, where n is an integer.
To solve the equation cos(x) = -1/√2, we need to determine the values of x that satisfy this equation.
Since the cosine function is negative in the second and third quadrants, we can find the reference angle whose cosine is 1/√2 and then find the corresponding angles in those quadrants.
The reference angle whose cosine is 1/√2 is π/4 (45 degrees).
In the second quadrant, the angle whose cosine is -1/√2 is π - π/4 = 3π/4 (135 degrees).
In the third quadrant, the angle whose cosine is -1/√2 is 2π - π/4 = 7π/4 (315 degrees).
Therefore, the solutions to the equation cos(x) = -1/√2 are:
x = 3π/4 + 2πn, where n is an integer
x = 7π/4 + 2πn, where n is an integer.