Final answer:
To solve the trigonometric equation 2sin(theta) - sqrt(2) = 0 on the interval 0 ≤ theta < 2, we isolate sin(theta) by adding sqrt(2) to both sides and then dividing by 2. The solution is theta = 45 degrees, 135 degrees.
Step-by-step explanation:
To solve the trigonometric equation 2sin(theta) - sqrt(2) = 0 on the interval 0 ≤ theta < 2, we need to isolate sin(theta). Start by adding sqrt(2) to both sides of the equation to get 2sin(theta) = sqrt(2). Then, divide both sides by 2 to get sin(theta) = sqrt(2)/2. So theta can be determined using the inverse sine function: theta = sin¯¹(sqrt(2)/2).
Since sin¯¹(sqrt(2)/2) equals 45 degrees or π/4 radians, theta can be equal to either 45 degrees or 135 degrees. However, we need to find the values of theta on the interval 0 ≤ theta < 2. Therefore, the solution to the equation is theta = 45 degrees, 135 degrees.