Question

Solve 2sin(2x) - 5 = -4 from [0,2π)
a) x = π/2
b) x = π
c) x = 3π/2
d) x = 0

Answer 1

To solve the equation 2sin(2x) - 5 = -4 from [0, 2π), isolate the term with the sine function, find the values of x that satisfy the equation, and consider the given interval to determine the correct solutions.

Step-by-step explanation:

To solve the equation 2sin(2x) - 5 = -4 from [0, 2π), we can start by isolating the term with the sine function. Adding 5 to both sides of the equation, we get 2sin(2x) = 1. Dividing by 2, we have sin(2x) = 1/2.

The next step is to find the values of x that satisfy this equation. We can use the unit circle or inverse trigonometric functions to do this. The solution is x = π/6 or x = 5π/6.

However, we need to find the values of x in the interval [0, 2π). So, the correct answer is x = π/6 and x = 5π/6.