What is the general solution for 2-2sin(θ)=4 ?

The general solution for 2-2sin(θ)=4 is θ=(3pi)/2+2pin

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2-2sin(θ)=4

2 - 2 sin (θ) = 4

θ = \frac{3 π}{2} + 2 πn

Degrees

θ = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

2 - 2 sin (θ) = 4

Move

2

to the right side

2 - 2 sin (θ) = 4

Subtract

2

from both sides

2 - 2 sin (θ) - 2 = 4 - 2

Simplify

- 2 sin (θ) = 2

- 2 sin (θ) = 2

Divide both sides by

- 2

- 2 sin (θ) = 2

Divide both sides by

- 2

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

Simplify

sin (θ) = - 1

sin (θ) = - 1

General solutions for

sin (θ) = - 1

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{3 π}{2} + 2 πn

θ = \frac{3 π}{2} + 2 πn

(sin (x))^{2} = 0

tan^{2} (x) sin (x) - \frac{sin ( x )}{3} = 0

cot^{2} (a) = cos^{2} (a) (cot (a) cos (a))^{2}

1 + cot^{2} (x) = 8 sin (x)

4 sin^{2} (x) = 8 sin^{2} (\frac{x}{2})

What is the general solution for 2-2sin(θ)=4 ?
The general solution for 2-2sin(θ)=4 is θ=(3pi)/2+2pin