Question

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

Answer 1

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]}