Solve the equation sin(x) = 0.5 for x in the interval [0, 2π].

₹0.0

Question: Solve the equation sin(x) = 0.5 for x in the interval [0, 2π].

Options:

Correct Answer: π/6

Solution:

The solutions are x = π/6 and x = 5π/6 in the interval [0, 2π].

Solve the equation sin(x) = 0.5 for x in the interval [0, 2π].

Solve the equation sin(x) = 0.5 for x in the interval [0, 2π].

Correct Answer: x = π/6 and x = 5π/6

Step 1: Understand the equation sin(x) = 0.5. We need to find the values of x where the sine of x equals 0.5.
Step 2: Recall the unit circle and the values of sine for common angles. The sine of an angle is 0.5 at specific angles.
Step 3: Identify the angles where sin(x) = 0.5. These angles are π/6 and 5π/6.
Step 4: Check if these angles are within the interval [0, 2π]. Both π/6 and 5π/6 are within this interval.
Step 5: Write down the solutions. The solutions to the equation sin(x) = 0.5 in the interval [0, 2π] are x = π/6 and x = 5π/6.

Trigonometric Equations – The question tests the ability to solve basic trigonometric equations, specifically using the sine function.
Unit Circle – Understanding the unit circle is essential for identifying angles where sine takes specific values.
Interval Notation – The problem requires solutions to be found within a specified interval, emphasizing the importance of considering the domain.