i need help for this question

Question

Solve  for the four smallest positive solutions.

Answer 1

Given:

7 sin( 4πx ) = 4

Find:

x = ?, ?, ?, ?

Solution:

7 sin( 4πx ) = 4

sin( 4πx ) = 4/7

4πx = sin^-1 ( 4/7 ) + 2πk (with k being the set of all real integers)

4πx = ( 2n + 1 )π - sin^-1 (4/7) (with n being the set of all real integers)

x = [ sin^-1 ( 4/7 ) / 4π ] + k/2

x = ( 2n + 1 ) / 4 - [ sin^-1 (4/7) / 4π ]

My calculator evaluates:

sin^-1 (4/7) ≈ 0.608 radians ≈ 34.85°

∴ x ≈ 0.0484, 0.202, 0.5484, 0.702 (answers for if you do radians)

∴ x ≈ 2.77, 11.55, 31.42, 40.20 (answers for if you do degrees)