How do you sketch a graph of the function: f(x) = pi / 2 + arctan xf(x)=π2+arctanx?

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)x=f1(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 = xtan(yπ2)=coty=x. So, the inverse is

x =- cot y.x=coty.

For the limits, as arctan x in (-pi/2, pi/2) arctanx(π2,π2),

x in ( -oo, oo ) and y = pi/2 + arctan xx(,)andy=π2+arctanx, for y in (-pi/2, pi/2)y(π2,π2)

Ax y to 0, x to -ooy0,x and as y to pi, x to ooyπ,x.

The y-intercept js are pi/2π2.

Extended graph for y = pi/2+(kpi + arctan x )y=π2+(kπ+arctanx), k =0, +-1, +-2,

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