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

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

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sin(α)=-1

sin (α) = - 1

α = \frac{3 π}{2} + 2 πn

Degrees

α = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (α) = - 1

General solutions for

sin (α) = - 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}

α = \frac{3 π}{2} + 2 πn

α = \frac{3 π}{2} + 2 πn

2 cos^{2} (a) + cos (a) - 1 = 0

6 sin (t) = 3

arctan (e^{x}) = \frac{π}{4}

csc^{2} (x) + 2 cos (x) + 1 = 0

2 cos^{2} (2 x) + 3 cos (2 x) - 2 = 0

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