Find the exact value of arctan (sin (π/2)). Explain your reasoning.

Solution:

Arctangent (Arctan) function is defined as :

y = tan^-1x is the value in (-π/2, π/2) for which tan y = x.

The graph of y = tan^-1x is also symmetric about the origin.

Algebraically this means that

tan^-1(-x ) = -tan^-1x

The arctangent is an odd function.

let us evaluate arctan (sin (π/2).

It can be written as:

y = tan^-1(sin(π/2)) [ on replacing x by sin(π/2) ]

sin(π/2) = tan y

We know that sin(π/2) = 1, hence we can write,

1 = tan y

Hence y = π/4(we know that tan(π/4) = 1)

Therefore arctan (sin (π/2) = π/4

---

Find the exact value of arctan (sin (π/2)). Explain your reasoning.

Summary:

The exact value of arctan (sin (π/2)) is π/4. The graph of y = tan^-1x is also symmetric about the origin.