What is the general solution for 0=1+sin(θ) ?

The general solution for 0=1+sin(θ) is θ=(3pi)/2+2pin

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0=1+sin(θ)

0 = 1 + sin (θ)

θ = \frac{3 π}{2} + 2 πn

Degrees

θ = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

0 = 1 + sin (θ)

Switch sides

1 + sin (θ) = 0

Move

1

to the right side

1 + sin (θ) = 0

Subtract

1

from both sides

1 + sin (θ) - 1 = 0 - 1

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

2 cos (2 x) - cos (x) - 1 = 0

tan (x) \cdot tan (2 x) = 1

cos (x) cot (x) - 3 (1 - sin (x)) = 0

18 = \frac{1}{2} \cdot 9 \cdot 5 \cdot sin (θ)

2 cos^{2} (x) = cos^{2} (x)

What is the general solution for 0=1+sin(θ) ?
The general solution for 0=1+sin(θ) is θ=(3pi)/2+2pin