What is the general solution for sin(x-pi/4)= 1/2 ?

The general solution for sin(x-pi/4)= 1/2 is x=2pin+(5pi)/(12),x=2pin+(13pi)/(12)

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sin(x-pi/4)= 1/2

sin (x - \frac{π}{4}) = \frac{1}{2}

x = 2 πn + \frac{5 π}{12}, x = 2 πn + \frac{13 π}{12}

Solution steps

sin (x - \frac{π}{4}) = \frac{1}{2}

General solutions for

sin (x - \frac{π}{4}) = \frac{1}{2}

x - \frac{π}{4} = \frac{π}{6} + 2 πn, x - \frac{π}{4} = \frac{5 π}{6} + 2 πn

Solve

x - \frac{π}{4} = \frac{π}{6} + 2 πn : x = 2 πn + \frac{5 π}{12}

Solve

x - \frac{π}{4} = \frac{5 π}{6} + 2 πn : x = 2 πn + \frac{13 π}{12}

x = 2 πn + \frac{5 π}{12}, x = 2 πn + \frac{13 π}{12}

3 sin (2 x) - \frac{3}{2} 3 = 0

- 12 sin (3 x) = 0

sin^{2} (θ) - \frac{1}{4} = 0

1 = sech (x)

sin^{2} (x) + 3 sin (x) = 0

What is the general solution for sin(x-pi/4)= 1/2 ?
The general solution for sin(x-pi/4)= 1/2 is x=2pin+(5pi)/(12),x=2pin+(13pi)/(12)