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

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

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-1=sin(x)

- 1 = sin (x)

x = \frac{3 π}{2} + 2 πn

Degrees

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

Solution steps

- 1 = sin (x)

Switch sides

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

2 sin^{2} (θ) = sin (θ)

3 sin (x) = 4 cos (x)

csc^{2} (x) - csc (x) + 9 = 11

4 sin (x) = - cos^{2} (x) + 4

csc^{2} (x) + csc (x) = 2

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