# #(sin )^(-1)# is the piecewise-wholesome inverse sine operator. The FCS y = #(sin )^(-1)(x+(sin )^(-1)(x+(sin )^(-1)(x+...)))#. How do you find the amplitude and the period, of this FCS wave?

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Definition of #(sin)^(-1)X# :

#Y = (sin)^(-1)X = kpi + (-1)^ksin^(-1)X, k = 0, +-1, +-2, +-3, ..., Y in [kpi-pi/2, kpi+pi/2]#

Definition of

##### 1 Answer

Axis of the wave: x + y = 0. Wave is bounded by the parallels

#### Explanation:

Definition of piecewise-wholesome

https://socratic.org/questions/on-what-interval-is-the-identity-sin-1-sin-x-x-valid#639442

The FCS wave, with axis

inflexion aligned in x + y = 0 and crests and troughs aligned in

graph{(x-sin y + y)(x+y)((x+y)^2-1)=0}

Graph of just one wave from

graph{(y-arcsin (x+y))(x+y)((x+y)^2-1)=0} .

The points of the meet with the axis are

The amplitude = half-width between

Period = 2 ( distance between two consecutive axial points)

Plots revealing a crust, a trough, period length and width.

graph{(x-sin y + y)(x-y)((x+y)^2-1)((x-3.14)^2+(y+3.14)^2-.01)((x+3.14)^2+(y-3.14)^2-.01)((x+0.57)^2+(y-1.57)^2 -.01)((x-0.57)^2+(y+1.57)^2 -.01)((x-0.5)^2 +(y-0.5)^2-.01)((x+0.5)^2 +(y+0.5)^2-.01)=0[-7 7 -3.5 3.5]}

Also see