I am given

Question

arcsin (sin 4pi)
do the arc sin and sin cancel out?
How do we solve this?

Answer 1

arcsin and sin are inverse operators, just like
squaring a number , then taking the square root.
e.g. √(6^2) = 6

arcsin(x ) will give you the angle so that sinØ = x
your calculator has been programmed to give you then angle closest to zero

e.g. arcsin(sin 30°) = 30°
(on your calculator, find sin 30° , you will get .5
now press 2ndF sin and get 30)

so

arcsin (sin 4pi)
= arcsin(0)
= 0, or π or 2π or 3π or 4π or ...