Question

What is the solution to the equation sin(x) = 0 in the interval 0 ≤ x < 2π?

A) x = 0
B) x = π
C) x = 2π
D) x = π/2

Answer 1

The solution to sin(x) = 0 in the interval 0 ≤ x < 2π is A) x = 0 and B) x = π, as sine is zero at these points within the given interval.

Step-by-step explanation:

The solution to the equation sin(x) = 0 in the interval 0 ≤ x < 2π is found by determining the angles at which the sine function equals zero. The sine function is zero at multiples of π, which within the given interval are:

• x = 0
• x = π

Therefore, the possible solutions are A) x = 0 and B) x = π. Option C) x = 2π is outside the interval since the interval is inclusive at 0 and exclusive at 2π. Option D) x = π/2 is not correct because the sine function equals 1 or -1 at these points, depending on the quadrant.