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

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Answer 1 · 2018-07-15T12:47:39

See graphs and explanation.

$y = π arcsin (4 x)$ $y = pi arcsin (4 x )$ . Inversely, $x = (\frac{1}{4}) sin (\frac{y}{π})$ $x = (1/4) sin ( y/pi )$ .

The y-axis is the axis of this wave.

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

Amplitude =1/4 $\Rightarrow | x | \leq 0.25 .$ $rArr abs x <= 0.25.$ .

The range : $y \in [- \frac{{(π)}^{2}}{2}, \frac{{(π)}^{2}}{2}] = [- 4.935, 4.935]$ $y in [-(pi)^2/2, (pi)^2/2 ] = [ - 4.935, 4.935 ]$ .

Domain ; $x \in [- \frac{1}{4}, \frac{1}{4}]$ $x in [ -1/4, 1/4 ]$ .

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

limits, attributed to the convention

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

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

common-to-both inverse $x = (\frac{1}{4}) sin (\frac{y}{π})$ $x = (1/4) sin (y/pi )$ . Here, the inverse is

wholesome and, by sliding the graph $↑ d a$ $uarr datt$ , you can see the

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

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

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 ${(sin)}^{- 1}$ $(sin)^(-1 )$ operator and display display

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

.

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