What is the general solution for 8|sin(pix)-1/4 |+1=7 ?

The general solution for 8|sin(pix)-1/4 |+1=7 is x= 7/6+2n,x= 11/6+2n,x= 1/2+2n

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8|sin(pix)-1/4 |+1=7

8 sin (π x) - \frac{1}{4} + 1 = 7

x = \frac{7}{6} + 2 n, x = \frac{11}{6} + 2 n, x = \frac{1}{2} + 2 n

Solution steps

8 sin (π x) - \frac{1}{4} + 1 = 7

Solve by substitution

sin (π x) = - \frac{1}{2} or sin (π x) = 1

sin (π x) = - \frac{1}{2} : x = \frac{7}{6} + 2 n, x = \frac{11}{6} + 2 n

sin (π x) = 1 : x = \frac{1}{2} + 2 n

Combine all the solutions

x = \frac{7}{6} + 2 n, x = \frac{11}{6} + 2 n, x = \frac{1}{2} + 2 n

8 sin^{2} (u) + 6 sin (u) - 9 = 0

sin (x) = 2 tan (x)

cos (θ) = \frac{1}{5}

sin (\frac{x}{2}) - cos (x) = 0

3 sin (x) = 3 - 3 cos (x)

What is the general solution for 8|sin(pix)-1/4 |+1=7 ?
The general solution for 8|sin(pix)-1/4 |+1=7 is x= 7/6+2n,x= 11/6+2n,x= 1/2+2n