How do you sketch the graph of f(x)=piarcsin(4x)?

1 Answer
Jul 15, 2018

See graphs and explanation.

Explanation:

y = pi arcsin (4 x ). Inversely, x = (1/4) sin ( y/pi ).

The y-axis is the axis of this wave.

The wave-period = #(2pi)/(1/pi) = 2(pi)^2 = 19.74, nearly.

Amplitude =1/4 rArr abs x <= 0.25..

The range : y in [-(pi)^2/2, (pi)^2/2 ] = [ - 4.935, 4.935 ].

Domain ; x in [ -1/4, 1/4 ].

See the graph of y = pi arcsin (4 x ), within the above guarding

limits, attributed to the convention

arcsin ( 4 x ) in [ - pi/2, pi/2 ].
graph{y-3.14 arcsin (4x ) = 0}

Now see the graph for y = pi (sin )^( -1 )( 4x ), using the

common-to-both inverse x = (1/4) sin (y/pi ). Here, the inverse is

wholesome and, by sliding the graph uarr datt , you can see the

pixel\march to +- oo. This is not possible in the other graph

above, for .y = pi arcsin (4 x )..

graph{x-0.25 sin( y / 3.14)=0[ -1 1 -40 40] }

I expect that the hand calculators would soon use the

piecewise-wholesome (sin)^(-1 ) operator and display display

(sin)^(-1)(sin (-120^o)) as -120^o and not - 60^o, ..

.