Trigonometric function symmetry If f (x) = sin (π / 4 x + π / 6), G (x) is symmetric with respect to x = 1, then G (x) is obtained There is also an analytic expression of y = 3sin (π / 2x + π / 6) with respect to x = 2 π symmetry

Trigonometric function symmetry If f (x) = sin (π / 4 x + π / 6), G (x) is symmetric with respect to x = 1, then G (x) is obtained There is also an analytic expression of y = 3sin (π / 2x + π / 6) with respect to x = 2 π symmetry

(1) If f (x) = sin (π / 4 x + π / 6) = sin π / 4 (x + 2 / 3) g (x) and f (x) are symmetric with respect to x = 1, then G (x) = f (2-x) then G (x) = sin π / 4 (2-x + 2 / 3) = sin (2 π / 3 - π / 4 x) (2) let the analytic expression of symmetry be g (x), and the original analytical expression be f (x), as above, G (x) = f (4 π - x), and then substitute it