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

1 Answer
Jul 15, 2018

See graphs and explanation.

Explanation:

y=πarcsin(4x). Inversely, x=(14)sin(yπ).

The y-axis is the axis of this wave.

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

Amplitude =1/4 |x|0.25..

The range : y[(π)22,(π)22]=[4.935,4.935].

Domain ; x[14,14].

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

limits, attributed to the convention

arcsin(4x)[π2,π2].
graph{y-3.14 arcsin (4x ) = 0}

Now see the graph for y=π(sin)1(4x), using the

common-to-both inverse x=(14)sin(yπ). Here, the inverse is

wholesome and, by sliding the graph da, you can see the

pixel\march to ±. This is not possible in the other graph

above, for .y=πarcsin(4x)..

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(120o)) as 120o and not 60o, ..

.