Question

Solve for all angles in the interval [0, 2π): 2sin(x) - 1 = 0.

a) x = π/6
b) x = 5π/6
c) x = π/2
d) x = 3π/2

Answer 1

To solve the equation 2sin(x) - 1 = 0, isolate the sin(x) term by adding 1 to both sides and dividing by 2. The angles in the interval [0, 2π) that satisfy sin(x) = 1/2 are x = π/6 and x = 5π/6.

Step-by-step explanation:

To solve the equation 2sin(x) - 1 = 0, we need to isolate the sin(x) term. First, add 1 to both sides of the equation: 2sin(x) = 1. Then, divide both sides by 2 to get sin(x) = 1/2. Now we need to find the angles in the interval [0, 2π) that have a sine value of 1/2. The angles that satisfy this are x = π/6 and x = 5π/6.