# How do I find the range of arcsin when the range IS affected by translation? This problem has 3x=arcsin(1/2f(x)) but I'm more concerned with the general rules.

##### 1 Answer

See details..

#### Explanation:

With

( If c is added to x, then

So,

Inversely,

If you like to do inversion to this inversion, what you get is the

piecewise wholesome inversion ( here I insist on the use of

my piecewise wholesome inverse operator

For the graph of this wholesome inverse, use

includes the bit, for the given equation.

See graphical depiction, for both.

graph{(x - 1/3 arcsin (y/2 ))(x-pi/6)(x+pi/6)=0}

The sine wave is in-between

graph{(y - 2 sin (3x))(y-2)(y+2)=0}

So, there is an immediate need to be serious about caring my

piecewise wholesome operator that is relevant to all time-oriented

x giving natural progressive oscillations, and likewise, in rotations

and revolutions, in this Universe. I had discussed this matter many

a time, in my answers,