Find the solutions of the equation 2sin(x) + √3 = 0.
Correct Answer: x = 7π/6 and 11π/6
- Step 1: Start with the equation 2sin(x) + √3 = 0.
- Step 2: Isolate sin(x) by subtracting √3 from both sides: 2sin(x) = -√3.
- Step 3: Divide both sides by 2 to solve for sin(x): sin(x) = -√3/2.
- Step 4: Identify the angles where sin(x) equals -√3/2. These angles are in the third and fourth quadrants.
- Step 5: The angles that satisfy sin(x) = -√3/2 are x = 7π/6 and x = 11π/6.
- Step 6: Therefore, the solutions to the equation are x = 7π/6 and x = 11π/6.
- Trigonometric Equations – The question tests the ability to solve equations involving trigonometric functions, specifically the sine function.
- Unit Circle – Understanding the unit circle is essential for identifying angles where the sine function takes specific values.
- Quadrants of the Unit Circle – Recognizing in which quadrants the sine function is negative is crucial for finding all solutions.
