Find the exact value of sin(1/2arcsin(-7/25))

Answer 1

suspect you mean
sin[ (1/2) arc sin -7/25) ]

draw your right triangle
call our angle A in quadrant 3 or 4 use 3
sides are -7 and -24, hypotenuse = 25
sinA = -7/25
cosA = -24/25

Half angle
sin (.5A) = - sqrt( [1-cosA]/2)
= -sqrt( [ 1/25 ] /2 )
= -(1/5)sqrt (1/2)