That is not Calculus.
sin ( 5 π / 4 ) = sin ( 4 π / 4 + π / 4 ) = sin ( π + π / 4 )
Since:
sin ( π + θ ) = - sin θ
sin ( 5 π / 4 ) = sin ( π + π / 4 ) = - sin ( π / 4 ) = - 1 / √ 2
The range of sin x :
−1 ≤ sin x ≤ 1
sin ( - π / 2 ) = - 1 , sin ( π / 2 ) = 1
So x must be in interval:
x ∈ [ - π / 2, π / 2 ]
The only angle in this interval whose sine is - 1 / √ 2 is x = - π / 4
because - π / 2 < - π / 4 < π / 2
So the solution is:
x = - π / 4
How do you solve: arcsin(sin 5pi/4)
2 answers
arcsin [ sin ( 5 π / 4 ) ] = - π / 4