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

The general solution for sin(1-2x)=1 is x=-pin+1/2-pi/4

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sin(1-2x)=1

Solution

sin (1 - 2 x) = 1

Solution

x = - πn + \frac{1}{2} - \frac{π}{4}

Degrees

x = - 16.35211 \dots^{\circ} - 18 0^{\circ} n

Solution steps

sin (1 - 2 x) = 1

General solutions for

sin (1 - 2 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}

1 - 2 x = \frac{π}{2} + 2 πn

1 - 2 x = \frac{π}{2} + 2 πn

Solve

1 - 2 x = \frac{π}{2} + 2 πn : x = - πn + \frac{1}{2} - \frac{π}{4}

1 - 2 x = \frac{π}{2} + 2 πn

Move

1

to the right side

1 - 2 x = \frac{π}{2} + 2 πn

Subtract

1

from both sides

1 - 2 x - 1 = \frac{π}{2} + 2 πn - 1

Simplify

- 2 x = \frac{π}{2} + 2 πn - 1

- 2 x = \frac{π}{2} + 2 πn - 1

Divide both sides by

- 2

- 2 x = \frac{π}{2} + 2 πn - 1

Divide both sides by

- 2

\frac{- 2 x}{- 2} = \frac{\frac{π}{2}}{- 2} + \frac{2 πn}{- 2} - \frac{1}{- 2}

Simplify

\frac{- 2 x}{- 2} = \frac{\frac{π}{2}}{- 2} + \frac{2 πn}{- 2} - \frac{1}{- 2}

Simplify

\frac{- 2 x}{- 2} : x

\frac{- 2 x}{- 2}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{π}{2}}{- 2} + \frac{2 πn}{- 2} - \frac{1}{- 2} : - πn + \frac{1}{2} - \frac{π}{4}

\frac{\frac{π}{2}}{- 2} + \frac{2 πn}{- 2} - \frac{1}{- 2}

Group like terms

= - \frac{1}{- 2} + \frac{2 πn}{- 2} + \frac{\frac{π}{2}}{- 2}

\frac{1}{- 2} = - \frac{1}{2}

\frac{1}{- 2}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{1}{2}

\frac{2 πn}{- 2} = - πn

\frac{2 πn}{- 2}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= - πn

= - (- \frac{1}{2}) - πn + \frac{\frac{π}{2}}{- 2}

Apply rule

- (- a) = a

= \frac{1}{2} - πn + \frac{\frac{π}{2}}{- 2}

Group like terms

= - πn + \frac{1}{2} + \frac{\frac{π}{2}}{- 2}

\frac{\frac{π}{2}}{- 2} = - \frac{π}{4}

\frac{\frac{π}{2}}{- 2}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{π}{2}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

\frac{\frac{π}{2}}{2} = \frac{π}{2 \cdot 2}

= - \frac{π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= - \frac{π}{4}

= - πn + \frac{1}{2} - \frac{π}{4}

x = - πn + \frac{1}{2} - \frac{π}{4}

x = - πn + \frac{1}{2} - \frac{π}{4}

x = - πn + \frac{1}{2} - \frac{π}{4}

x = - πn + \frac{1}{2} - \frac{π}{4}

Popular Examples

4sin(4x)=0

4 sin (4 x) = 0

5cos(x)+2=cos(x)

5 cos (x) + 2 = cos (x)

2tan(4x)+1=3tan(4x)

2 tan (4 x) + 1 = 3 tan (4 x)

sec(x)=-5,pi<x<(3pi)/2

sec (x) = - 5, π < x < \frac{3 π}{2}

sin(θ/2)= 3/5

sin (\frac{θ}{2}) = \frac{3}{5}

Frequently Asked Questions (FAQ)

What is the general solution for sin(1-2x)=1 ?
The general solution for sin(1-2x)=1 is x=-pin+1/2-pi/4