What is the general solution for sin(x)(1-2cos(x))=0 ?

The general solution for sin(x)(1-2cos(x))=0 is x=2pin,x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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sin(x)(1-2cos(x))=0

sin (x) (1 - 2 cos (x)) = 0

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) (1 - 2 cos (x)) = 0

Solving each part separately

sin (x) = 0 or 1 - 2 cos (x) = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

General solutions for

sin (x) = 0

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 = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

1 - 2 cos (x) = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

1 - 2 cos (x) = 0

Move

1

to the right side

1 - 2 cos (x) = 0

Subtract

1

from both sides

1 - 2 cos (x) - 1 = 0 - 1

Simplify

- 2 cos (x) = - 1

- 2 cos (x) = - 1

Divide both sides by

- 2

- 2 cos (x) = - 1

Divide both sides by

- 2

\frac{- 2 cos ( x )}{- 2} = \frac{- 1}{- 2}

Simplify

cos (x) = \frac{1}{2}

cos (x) = \frac{1}{2}

General solutions for

cos (x) = \frac{1}{2}

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

4 cos^{2} (x) + 3 cos (x) = 1

sin (x) = 4 cos (x)

7 cos (x) = 0

sin (θ) = \frac{3 13}{13}, sec (θ)

sin (y) = \frac{1}{2}

What is the general solution for sin(x)(1-2cos(x))=0 ?
The general solution for sin(x)(1-2cos(x))=0 is x=2pin,x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin