Solve 6 sin (𝝅/2 ×)=3 for the four smallest positive solutions

Question

I've been stuck on this equation for a while. Anyone know how to solve this? If possible, please explain how you solved it.

Answer 1

6sin(π/2⋅x) = 3

sin(π/2⋅x) = 1/2

From the unit circle, the sine values that equal 1/2 have the solution set x = π/6+2πn, 5π/6+2πn

π/2⋅x = π/6+2πn, 5π/6+2πn

x = 1/3+4n, 5/3+4n

Since we are looking for the 4 smallest positive solutions, we would need to plug in n=0 and n=1:

x = 1/3+4(0), 5/3+4(0)

x = 1/3, 5/3

x = 1/3+4(1), 5/3+4(1)

x = 13/3, 17/3

Thus, the 4 smallest positive solutions are x = {1/3, 5/3, 13/3, 17/3}

Hope this helped!