Final answer:
The values of x in the interval [0, 2] that satisfy the equation 16 cos(x) - 8 = 0 are x = π/3.
Step-by-step explanation:
The given equation is 16 cos(x) - 8 = 0 and we need to find all values of x in the interval [0, 2] that satisfy the equation.
To solve the equation, we can isolate the cosine term by adding 8 to both sides: 16 cos(x) = 8.
Next, divide both sides by 16 to get cos(x) = 0.5.
Using the unit circle or a calculator, we find two angles that have a cosine of 0.5: x = π/3 and x = 5π/3.
Since we are looking for values of x in the interval [0, 2], the solution set is x = π/3.