Answer :
Answer:
Step-by-step explanation:
Given the expression sin(11pi/2 +x) =-1/2
Take the arcsin of both sides
sin⁻¹[sin(11pi/2 +x)] =sin⁻¹(-1/2)
11pi/2 + x = -30
x = -pi/6 - 11pi/2
Find the LCM
x = (-pi-33pi)/6
x = -34pi/6
x = -17pi/3
Since x is negative and sin is negative in the fourth quadrant
x = - 17pi/2
x = -1530⁰+1440⁰ (scaling down the angle)
x = -90
x = 360 - 90 (fourth quadrant)
x = 270⁰
x = 270pi/180
x = 27pi/18
x = 3pi/2
Hence x the solution of x is 3pi/2