What is the general solution for sin(x+pi/4)= 1/2 ,0<= x<= 2pi ?

The general solution for sin(x+pi/4)= 1/2 ,0<= x<= 2pi is x=(7pi)/(12),x=(23pi)/(12)

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sin(x+pi/4)= 1/2 ,0<= x<= 2pi

sin (x + \frac{π}{4}) = \frac{1}{2}, 0 \leq x \leq 2 π

x = \frac{7 π}{12}, x = \frac{23 π}{12}

Solution steps

sin (x + \frac{π}{4}) = \frac{1}{2}, 0 \leq x \leq 2 π

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{π}{12}

Solve

x + \frac{π}{4} = \frac{5 π}{6} + 2 πn : x = 2 πn + \frac{7 π}{12}

x = 2 πn - \frac{π}{12}, x = 2 πn + \frac{7 π}{12}

Solutions for the range

0 \leq x \leq 2 π

x = \frac{7 π}{12}, x = \frac{23 π}{12}

cos (2 x) + 7 cos (x) + 4 = 0

2 sec (θ) - 2 = 0

8 cos (2 θ) = 24 cos (θ) - 16

x, y = sin (x^{2})

2 sin^{2} (x) = 1 + sin (x)

What is the general solution for sin(x+pi/4)= 1/2 ,0<= x<= 2pi ?
The general solution for sin(x+pi/4)= 1/2 ,0<= x<= 2pi is x=(7pi)/(12),x=(23pi)/(12)