How do you sketch a graph of the function: f(x) = pi / 2 + arctan x?

1 Answer
Nov 23, 2016

See graphs and explanation.

Explanation:

For graph of y = f(x), where f involves inverse trigonometric

functions, use the x-explicit inverse x = f^(-1)(y). The graphs of

both are the same.

Graph of

graph{x tan y+1=0 [-3.14, 3.14, 0 3.14]}

tan (y-pi/2)= -cot y = x. So, the inverse is

x =- cot y.

For the limits, as arctan x in (-pi/2, pi/2) ,

x in ( -oo, oo ) and y = pi/2 + arctan x, for y in (-pi/2, pi/2)

Ax y to 0, x to -oo and as y to pi, x to oo.

The y-intercept js are pi/2.

Extended graph for y = pi/2+(kpi + arctan x ), k =0, +-1, +-2,

+-3... , with both x and y without limits.
graph{x tan y+1=0 [-50 50 -25 25]}