Question

Solve the equation sin x = -1/2 over the interval [0, 2π).

a) x = π/6
b) x = 5π/6
c) x = 7π/6
d) x = 11π/6

Answer 1

The equation sin x = -1/2 over the interval [0, 2π) has two solutions: x = 5π/6 and x = 7π/6. These angles correspond to the third and fourth quadrants where the sine value is negative.

Step-by-step explanation:

The question asks to solve the equation sin x = -1/2 over the interval [0, 2π). To find the values of x that satisfy this equation, we look for angles in the unit circle where the sine value is -1/2. In this case, the negative sign indicates that we are looking for angles in the third and fourth quadrants where the sine values are negative. From the reference angle π/6, we can determine that the solutions over the interval [0, 2π) are:

• b) x = 5π/6 - This angle is in the third quadrant where sine is negative, and it corresponds to the reference angle π/6.
• c) x = 7π/6 - This angle is also in the third quadrant and corresponds to the same reference angle π/6.

The other options (a) and (d) do not satisfy the condition sin x = -1/2 in the given interval.