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

Degrees

θ = 21 0^{\circ} + 36 0^{\circ} n, θ = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

3 = 2 - 2 sin (θ)

Switch sides

2 - 2 sin (θ) = 3

Move

2

to the right side

2 - 2 sin (θ) = 3

Subtract

2

from both sides

2 - 2 sin (θ) - 2 = 3 - 2

Simplify

- 2 sin (θ) = 1

- 2 sin (θ) = 1

Divide both sides by

- 2

- 2 sin (θ) = 1

Divide both sides by

- 2

\frac{- 2 sin ( θ )}{- 2} = \frac{1}{- 2}

Simplify

sin (θ) = - \frac{1}{2}

sin (θ) = - \frac{1}{2}

General solutions for

sin (θ) = - \frac{1}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

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

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