What is the general solution for -6=-2+8sin(θ+pi/4) ?

The general solution for -6=-2+8sin(θ+pi/4) is θ=2pin+(11pi)/(12),θ=2pin+(19pi)/(12)

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-6=-2+8sin(θ+pi/4)

- 6 = - 2 + 8 sin (θ + \frac{π}{4})

θ = 2 πn + \frac{11 π}{12}, θ = 2 πn + \frac{19 π}{12}

Solution steps

- 6 = - 2 + 8 sin (θ + \frac{π}{4})

Switch sides

- 2 + 8 sin (θ + \frac{π}{4}) = - 6

Move

2

to the right side

8 sin (θ + \frac{π}{4}) = - 4

Divide both sides by

8

sin (θ + \frac{π}{4}) = - \frac{1}{2}

General solutions for

sin (θ + \frac{π}{4}) = - \frac{1}{2}

θ + \frac{π}{4} = \frac{7 π}{6} + 2 πn, θ + \frac{π}{4} = \frac{11 π}{6} + 2 πn

Solve

θ + \frac{π}{4} = \frac{7 π}{6} + 2 πn : θ = 2 πn + \frac{11 π}{12}

Solve

θ + \frac{π}{4} = \frac{11 π}{6} + 2 πn : θ = 2 πn + \frac{19 π}{12}

θ = 2 πn + \frac{11 π}{12}, θ = 2 πn + \frac{19 π}{12}

0 = 12 cos (\frac{π}{3} x) + 8

0 = sin (t) + 2 sin (2 t)

sin (x) = - 0.9

1 = tan (\frac{π}{4} + c)

cos (θ) - cos (3 θ) = 0

What is the general solution for -6=-2+8sin(θ+pi/4) ?
The general solution for -6=-2+8sin(θ+pi/4) is θ=2pin+(11pi)/(12),θ=2pin+(19pi)/(12)