What is the general solution for 0.5=1-sin(θ) ?

The general solution for 0.5=1-sin(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin

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0.5=1-sin(θ)

0.5 = 1 - sin (θ)

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Degrees

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

0.5 = 1 - sin (θ)

Switch sides

1 - sin (θ) = 0.5

Move

1

to the right side

1 - sin (θ) = 0.5

Subtract

1

from both sides

1 - sin (θ) - 1 = 0.5 - 1

Simplify

- sin (θ) = - 0.5

- sin (θ) = - 0.5

Divide both sides by

- 1

- sin (θ) = - 0.5

Divide both sides by

- 1

\frac{- sin ( θ )}{- 1} = \frac{- 0.5}{- 1}

Simplify

sin (θ) = 0.5

sin (θ) = 0.5

General solutions for

sin (θ) = 0.5

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{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

What is the general solution for 0.5=1-sin(θ) ?
The general solution for 0.5=1-sin(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin