What is the general solution for 1-2sin(x)=-1 ?

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

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1-2sin(x)=-1

1 - 2 sin (x) = - 1

x = \frac{π}{2} + 2 πn

Degrees

x = 9 0^{\circ} + 36 0^{\circ} n

Solution steps

1 - 2 sin (x) = - 1

Move

1

to the right side

1 - 2 sin (x) = - 1

Subtract

1

from both sides

1 - 2 sin (x) - 1 = - 1 - 1

Simplify

- 2 sin (x) = - 2

- 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) = 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{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

4 tan^{2} (x) + sec (x) = - 2 tan^{2} (x) + sec^{2} (x) - 3

sin (α) = 0, 8 y (α) α < 9 0^{\circ}, cos (α)

cos (θ) = \frac{2}{5}, tan (θ), 0 < θ < \frac{π}{2}, π < θ < 2 π

sin (θ) = \frac{13}{14}

7 cot (z) + tan (z) = 7 csc (z)

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