On the axis of symmetry in mathematics! Why do we say that the symmetry axis of a line segment has its own straight line besides its vertical bisector? If we say that the two sides of the line segment can completely coincide with the straight line, but the line segment can not be folded? Isn't this a contradiction?

On the axis of symmetry in mathematics! Why do we say that the symmetry axis of a line segment has its own straight line besides its vertical bisector? If we say that the two sides of the line segment can completely coincide with the straight line, but the line segment can not be folded? Isn't this a contradiction?

As shown in the picture &My picture is exaggerated The first explanation: if a point is on the axis of symmetry, then its corresponding point is also on the axis of symmetry. The second explanation: the theorem of axisymmetry is that if a figure is folded along a line, the two sides of the line

What line should be used to draw the axis of symmetry in mathematics

Dotted line

F (x) = 5sin (2x - π / 3) x ∈ r to find the symmetry axis and center of F (x) monotone interval

From 2K π - π / 2 ≤ 2x - π / 3 ≤ 2K π + π / 2, K ∈ Z, we get: K π - π / 12 ≤ x ≤ K π + 5 π / 12, K ∈ Z, monotone increasing interval [K π - π / 12, K π + 5 π / 12] K ∈ Z, monotone decreasing interval [K π + 5 π / 12, K π + 11 π / 12] K ∈ Z, from 2x - π / 3 = k π + π / 2, K ∈ Z, we get symmetry axis X = k π / 2 + 5 π / 12, K ∈ Z

If a symmetry axis equation of function y = - 5sin (2x + Φ) is x = - 2 π / 3, then Φ =?

∵ f (x) = - 5sin (2x + φ) = 5cos (π / 2 + 2x + φ) let 5cos (π / 2 + 2x + φ) = 5 = = > cos (π / 2 + 2x + φ) = 1 = = > π / 2 + 2x + φ = 2K π = = > 2x = 2K π - π / 2 - φ = = > x = k π - π / 4 - φ / 2 take k = 0, x = - π / 4 - φ / 2 - π / 4 - φ / 2 = - 2 π / 3 = = > φ / 2 = 2 π / 3 - π / 4 = 5 π / 12 ∵ φ = 5 π / 6