What is the general solution for sin(x+pi/4)=(sqrt(3))/2 ?

The general solution for sin(x+pi/4)=(sqrt(3))/2 is x=2pin+pi/(12),x=2pin+(5pi)/(12)

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sin(x+pi/4)=(sqrt(3))/2

sin (x + \frac{π}{4}) = \frac{3}{2}

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

Solution steps

sin (x + \frac{π}{4}) = \frac{3}{2}

General solutions for

sin (x + \frac{π}{4}) = \frac{3}{2}

x + \frac{π}{4} = \frac{π}{3} + 2 πn, x + \frac{π}{4} = \frac{2 π}{3} + 2 πn

Solve

x + \frac{π}{4} = \frac{π}{3} + 2 πn : x = 2 πn + \frac{π}{12}

Solve

x + \frac{π}{4} = \frac{2 π}{3} + 2 πn : x = 2 πn + \frac{5 π}{12}

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

2 sin (2 x) = - 3

sin (x) cos (x) - cos (x) = 0

tan (x) = \frac{5}{2}

4 sin (x) cos (x) = 3

3 sin (x) + 4 cos (x) = 2

What is the general solution for sin(x+pi/4)=(sqrt(3))/2 ?
The general solution for sin(x+pi/4)=(sqrt(3))/2 is x=2pin+pi/(12),x=2pin+(5pi)/(12)