How do you graph y = arcsec(x)?

1 Answer
Jul 17, 2018

See graph and my idiosyncratic explanation.

Explanation:

y = arcsec x = arc cos(1/x) ,

Conventionally limited ( for trigonometric arccos ) y in [ 0, pi ].

See the truncated-graph, with asymptote y = pi/2 and

the limiting lines y = 0 and y = pi.
graph{(y-arccos(1/x))(y-pi/2)(y-pi)(y)=0}

See the wholesome-inverse graph for y = (sec)^(-1)x,

using the inverse x = sec y

graph{(x cos y - 1)(x^2-0.25) = 0[-50 50 -25 25]}

You can see the effect of the small operator sec^(-1 becoming

great (sec)^(-1), like Universe before the Earth.

Observe in both the graphs that y notin ( - 1, 1 )

Please note, that piecewise/wholesome,

the graphs of y = f( x ) and x = f^( - 1 ) ( y ) are one and the same.