What is the general solution for -2sin(x)=-sqrt(2) ?

The general solution for -2sin(x)=-sqrt(2) is x= pi/4+2pin,x=(3pi)/4+2pin

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-2sin(x)=-sqrt(2)

- 2 sin (x) = - 2

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

Degrees

x = 4 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n

Solution steps

- 2 sin (x) = - 2

Divide both sides by

- 2

- 2 sin (x) = - 2

Divide both sides by

- 2

\frac{- 2 sin ( x )}{- 2} = \frac{- 2}{- 2}

Simplify

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

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

General solutions for

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

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{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

sin (π - x) = cos (\frac{3 π}{2} - x) + cos (π)

4 csc (x) + 8 = 0

2 cos (2 θ) + 3 = 2

sin (\frac{3 π}{2} - 2 x) = sin (x)

α, sin (α) - sin (β) = cos (β) - cos (α)

What is the general solution for -2sin(x)=-sqrt(2) ?
The general solution for -2sin(x)=-sqrt(2) is x= pi/4+2pin,x=(3pi)/4+2pin