Find exact value when its defined: arcsin(sin[5pi/4])?

0 ⤊

solution is -pi/4. please explain.

2007-04-22 20:14:16 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

arcsin(sin[5pi/4])
=arcsin(-sin[pi/4])
=arcsin(-sqrt(2)/2)
sinx= (-sqrt(2)/2
x=pi+pi/4=5pi/4

or

x=2pi-pi/4
=7pi/4
=-pi/4

2007-04-22 20:24:31 · answer #1 · answered by iyiogrenci 6 · 0⤊ 0⤋

-pi/4 is the principle value of this function (calculator value too)
I still think that the exact value of this function is 5pi/4
but books differ

2007-04-22 20:19:59 · answer #2 · answered by Maths Rocks 4 · 0⤊ 0⤋

sin^(-1)(sin 5π/4) = 5π/4

2007-04-22 20:27:22 · answer #3 · answered by Como 7 · 0⤊ 0⤋