Arccos(x^3/2)?

1 Answer
Jul 13, 2018

See explanation and graphs.

Explanation:

As per the conventional range,

#y = arccos( x^3 / 2 ) in [ 0, pi ]#. See graph, The upper end braces

#y = pi = 3.14#, nearly. .

graph{(y-arccos (x^3/2))(y-3.1416)=0[-4 4 0 4] }

Inversely,

#x = (2 cos y)^(1/3)#, with #-2^(1/3) ,<= x ,<= 2^(1/3) = 1.26#,

( amplitude of the wave ) nearly.#

x-period is #(2pi)/2 = pi rArr. x(y) = x ( y + pi )#

For the piecewise-wholesome inverse, # y = (cos)^(-1)(x^3/2)#,

see the wave form in infinitude, in the uniform-scale graph below,

flanked by #x = +- 1.26#..
graph{(x-(2cos y )^(1/3))(x^2-(1.26)^2)=0[-40 40 -20 20]}

Here, #- oo < y < oo# and #-1.26 < x < 1.26#.