In the following functions, the period is π, and the symmetric function of the image with respect to the line x = π / 3 is () A.y=2sin(x/2+π/3) B.y=2sin(x/2-π/3) C.y=2sin(2x+π/6) D.y=2sin(2x-π/3) The answer is to exclude AB with the definition first, the period is π, AB does not hold Then, x = π / 3 is the axis of symmetry, From term C, we can take the symmetric point (2 π / 3, - 1 / 2) of point (0, - 1 / 2) with respect to x = π / 3, and substitute x = 2 π / 3 into term C, then y = - 2 ≠ - 1 / 2 doubt! Q: Why shouldn't y = - 1 when x = 0 in the C-term (0, - 1 / 2)?

In the following functions, the period is π, and the symmetric function of the image with respect to the line x = π / 3 is () A.y=2sin(x/2+π/3) B.y=2sin(x/2-π/3) C.y=2sin(2x+π/6) D.y=2sin(2x-π/3) The answer is to exclude AB with the definition first, the period is π, AB does not hold Then, x = π / 3 is the axis of symmetry, From term C, we can take the symmetric point (2 π / 3, - 1 / 2) of point (0, - 1 / 2) with respect to x = π / 3, and substitute x = 2 π / 3 into term C, then y = - 2 ≠ - 1 / 2 doubt! Q: Why shouldn't y = - 1 when x = 0 in the C-term (0, - 1 / 2)?

Solution 1. Find two symmetrical points about the straight line x = π / 3 and substitute them into the function to see if y is equal
Such as points (0, Y1) and (2 π / 3, Y2)
(-2π/3,y1),(4π/3,y2)
See if Y1 equals Y2
The answer is wrong