What is the smallest positive value of a for which the line x = a is a line of symmetry of the graph of y = sin(2x − 4π3)?
- Aπ12
- B5π12
- C7π12
- D11π12
- E19π12
Show the answer and worked solution
answer · B
- Aπ12
- B5π12
- C7π12
- D11π12
- E19π12
A sine curve is symmetric about each of its peaks and troughs, and nowhere else, so the lines of symmetry are the vertical lines through the turning points. These occur when 2x − 4π3 = π2 + kπ, so 2x = 11π6 + kπ and x = 11π12 + kπ2. Taking k = −1 gives 11π12 − 6π12 = 5π12, and k = −2 would give a negative value, so the smallest positive one is 5π12.