The function y = 2Sin (3x + π / 6) image is shifted to the left by π / 6 units, and the function y = 2cos (3x + π / 6) image is obtained. Please explain whether this conclusion is correct

The function y = 2Sin (3x + π / 6) image is shifted to the left by π / 6 units, and the function y = 2cos (3x + π / 6) image is obtained. Please explain whether this conclusion is correct

The function y = 2Sin (3x + π / 6) image is shifted to the left by π / 6 units
∴y=2sin(3(x+π/6)+π/6)=2sin(π/2+(3x+π/6))=2cos(3x+π/6)

The image of the function y = 2Sin (3x + 1)

First, the image of y = sin (3x) is drawn by five point method;
Then shift it 1 / 3 unit to the left,
Then stretch 2 times longitudinally to make a sketch
Or directly use the five point drawing method, because it is also a periodic function, 2pi / 3 is the minimum positive period

The image of function y = 1 / 2Sin (2x - π / 6) can be regarded as the result of translating the image of function y = 1 / 2sin2x to units

Analysis: because y = 1 / 2Sin (2x - π / 6) = y = 1 / 2Sin [2 (x - π / 12)], the image of function y = 1 / 2Sin (2x - π / 6) can be seen as the result of translating the image of function y = 1 / 2sin2x to the right by π / 12 units