Question

Solve the trigonometric equation for all values 0 ≤ x < 2π:

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

Answer 1

To solve the trigonometric equation for all values 0 ≤ x < 2π, we need to find the values of x that satisfy the equation. The valid values of x that satisfy the equation are a) x = π, b) x = π/2, c) x = 3π/2, and d) x = 2π.

Step-by-step explanation:

To solve the trigonometric equation for all values 0 ≤ x < 2π, we need to find the values of x that satisfy the equation. Let's solve each option and see which values of x are valid.

a) x = π: Since sin(π) = 0, this value of x satisfies the equation.

b) x = π/2: Since sin(π/2) = 1, this value of x satisfies the equation.

c) x = 3π/2: Since sin(3π/2) = -1, this value of x satisfies the equation.

d) x = 2π: Since sin(2π) = 0, this value of x satisfies the equation.

Therefore, the valid values of x that satisfy the equation are a) x = π, b) x = π/2, c) x = 3π/2, and d) x = 2π.