what is arcsin(sin3)?

Question

i know arcsin is the inverse function of sin, and is 1-1 over the restricted domain of [-pi/2,pi/2].

how do i find arcsin(sin3) without using a calculator?

also, for what values of x is it true that arcsin(sinx)=x? and how do i show this?

thanks

Answer 1

arc sin(sin x) = x when x is between -pi/2 and pi/2

else we have to bring the range to -pi/2 to pi/2

arc sin (sin 3) = -(3 - pi) as 3 is close to pi

by adding or subtracting multiple of 2pi get the value from -pi/2 to 3pi/2
if it is between -pi/2 and +pi/2 it is the result else it is - (pi-x)

Answer 2

You have to find the angle whose sin is the sin of 3
as sin 3=0.1411 rad
sin x= 0.1411 and x=3+2kpi and x= (pi-3)+2kpi (k any integer)
It is true for all values of x in the restricted interva (-pi/2,pi/2) as in this interval the function arcsin is an increasing one

Answer 3

please see this
http://in.answers.yahoo.com/question/index;_ylt=Aml1fbADGJImXk7E0OuypJaQHQx.?qid=20070506031833AA6LS7W
if you have already read my question, then you will say that arcsin(sin x) is equal to x when a is in the resticted domain you just entered. secondly, there is no proof of arcsin(sin x) being equal to x for a certain value of x. the range from -π/2 and π/2 has been said to have that true. we could have taken another range. it is no mathematical fact of arcsin(sin x) being equal to x for a certain range of numbers. it aint got no proof.