Solve the equation cos(x) = -1/2 for x in the interval [0, 2π].
Practice Questions
Q1
Solve the equation cos(x) = -1/2 for x in the interval [0, 2π].
2π/3, 4π/3
π/3, 5π/3
π/2, 3π/2
0, π
Questions & Step-by-Step Solutions
Solve the equation cos(x) = -1/2 for x in the interval [0, 2π].
Correct Answer: x = 2π/3 and x = 4π/3
Step 1: Understand the equation cos(x) = -1/2. We need to find the values of x where the cosine of x equals -1/2.
Step 2: Recall the unit circle and the values of cosine. Cosine is negative in the second and third quadrants.
Step 3: Identify the reference angle. The reference angle for cos(x) = 1/2 is π/3 (60 degrees). Since we need cos(x) = -1/2, we will use the angles in the second and third quadrants.
Step 4: Find the angles in the second quadrant. The angle is π - π/3 = 2π/3.
Step 5: Find the angles in the third quadrant. The angle is π + π/3 = 4π/3.
Step 6: List the solutions. The solutions for x in the interval [0, 2π] are x = 2π/3 and x = 4π/3.
