What is the general solution for 3=2-2sin(θ) ?

The general solution for 3=2-2sin(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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3=2-2sin(θ)

3 = 2 - 2 sin (θ)

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

Solution steps

3 = 2 - 2 sin (θ)

Switch sides

2 - 2 sin (θ) = 3

Move

2

to the right side

- 2 sin (θ) = 1

Divide both sides by

- 2

sin (θ) = - \frac{1}{2}

General solutions for

sin (θ) = - \frac{1}{2}

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

sin (θ) = \frac{563}{2000}

6 sec (2 x) - 8 = 0

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

8 cos^{2} (x) = 2

arctan (t) + 1 = 1

What is the general solution for 3=2-2sin(θ) ?
The general solution for 3=2-2sin(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin