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

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

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1+sin(x)=0

1 + sin (x) = 0

x = \frac{3 π}{2} + 2 πn

Degrees

x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

1 + sin (x) = 0

Move

1

to the right side

1 + sin (x) = 0

Subtract

1

from both sides

1 + sin (x) - 1 = 0 - 1

Simplify

sin (x) = - 1

sin (x) = - 1

General solutions for

sin (x) = - 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}

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

sin^{2} (x) - \frac{1}{4} = 0

cos (x) = - \frac{1}{3}

tan (\frac{θ}{2} + \frac{π}{3}) = 1

2 sin (π θ) = 1

23 sin (\frac{x}{2}) = 3

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