Question

Hi,

Find the exact value of the following expression:

Sin^-1(1/radical2)

(Its inverse sin(1/radical2)

Direction -(Type your answers in interval notation. Type an exact answer using pi as need)

Please show how you got the answers so I can use this as a reference for others. THANK YOU.

Answer 1

There are no intervals involved.

since sin(π/4) = 1/√2

the principal value of arcsin,

Sin^-1(1/√2) = π/4

But, since there are many other angles,

sin^-1(1/√2) = π/4 or 3π/4

and since the period of sin(x) is 2π,

sin^-1(1/√2) = π/4 + 2nπ or 3π/4 + 2nπ

Or, since those values are in QI and QII, symmetric with the y-axis,

sin^-1(1/√2) = (4n+1)(π/2) ± π/4