What are the solutions of the equation cos(x) = -1/2?

What are the solutions of the equation cos(x) = -1/2?

Step 1: Understand the equation cos(x) = -1/2. This means we are looking for angles x where the cosine value is -1/2.
Step 2: Recall the unit circle and the values of cosine for common angles. The cosine of an angle is negative in the second and third quadrants.
Step 3: Identify the reference angle where cos(x) = 1/2. This reference angle is π/3 (or 60 degrees).
Step 4: Find the angles in the second and third quadrants that correspond to this reference angle. In the second quadrant, the angle is π - π/3 = 2π/3. In the third quadrant, the angle is π + π/3 = 4π/3.
Step 5: Write down the solutions. The solutions to the equation cos(x) = -1/2 are x = 2π/3 and x = 4π/3.

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