What is the general solution for sin(180/2-x)=0.8 ?

The general solution for sin(180/2-x)=0.8 is x=90-2pin-0.92729…,x=-pi+90-2pin+0.92729…

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Popular >

sin(180/2-x)=0.8

Solution

sin (\frac{180}{2} - x) = 0.8

Solution

x = 90 - 2 πn - 0.92729 \dots, x = - π + 90 - 2 πn + 0.92729 \dots

Degrees

x = 5103.49005 \dots^{\circ} - 36 0^{\circ} n, x = 5029.75025 \dots^{\circ} - 36 0^{\circ} n

Solution steps

sin (\frac{180}{2} - x) = 0.8

Apply trig inverse properties

sin (\frac{180}{2} - x) = 0.8

General solutions for

sin (\frac{180}{2} - x) = 0.8

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

\frac{180}{2} - x = arcsin (0.8) + 2 πn, \frac{180}{2} - x = π - arcsin (0.8) + 2 πn

\frac{180}{2} - x = arcsin (0.8) + 2 πn, \frac{180}{2} - x = π - arcsin (0.8) + 2 πn

Solve

\frac{180}{2} - x = arcsin (0.8) + 2 πn : x = 90 - 2 πn - arcsin (0.8)

\frac{180}{2} - x = arcsin (0.8) + 2 πn

Divide the numbers:

\frac{180}{2} = 90

90 - x = arcsin (0.8) + 2 πn

Move

90

to the right side

90 - x = arcsin (0.8) + 2 πn

Subtract

90

from both sides

90 - x - 90 = arcsin (0.8) + 2 πn - 90

Simplify

- x = arcsin (0.8) + 2 πn - 90

- x = arcsin (0.8) + 2 πn - 90

Divide both sides by

- 1

- x = arcsin (0.8) + 2 πn - 90

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{arcsin ( 0.8 )}{- 1} + \frac{2 πn}{- 1} - \frac{90}{- 1}

Simplify

\frac{- x}{- 1} = \frac{arcsin ( 0.8 )}{- 1} + \frac{2 πn}{- 1} - \frac{90}{- 1}

Simplify

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Apply the fraction rule:

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

= \frac{x}{1}

Apply rule

\frac{a}{1} = a

= x

Simplify

\frac{arcsin ( 0.8 )}{- 1} + \frac{2 πn}{- 1} - \frac{90}{- 1} : 90 - 2 πn - arcsin (0.8)

\frac{arcsin ( 0.8 )}{- 1} + \frac{2 πn}{- 1} - \frac{90}{- 1}

Group like terms

= - \frac{90}{- 1} + \frac{2 πn}{- 1} + \frac{arcsin ( 0.8 )}{- 1}

\frac{90}{- 1} = - 90

\frac{90}{- 1}

Apply the fraction rule:

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

= - \frac{90}{1}

Apply rule

\frac{a}{1} = a

= - 90

\frac{2 πn}{- 1} = - 2 πn

\frac{2 πn}{- 1}

Apply the fraction rule:

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

= - \frac{2 πn}{1}

Apply rule

\frac{a}{1} = a

= - 2 πn

= - (- 90) - 2 πn + \frac{arcsin ( 0.8 )}{- 1}

Apply rule

- (- a) = a

= 90 - 2 πn + \frac{arcsin ( 0.8 )}{- 1}

\frac{arcsin ( 0.8 )}{- 1} = - arcsin (0.8)

\frac{arcsin ( 0.8 )}{- 1}

Apply the fraction rule:

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

= - \frac{arcsin ( 0.8 )}{1}

Apply rule

\frac{a}{1} = a

= - arcsin (0.8)

= 90 - 2 πn - arcsin (0.8)

x = 90 - 2 πn - arcsin (0.8)

x = 90 - 2 πn - arcsin (0.8)

x = 90 - 2 πn - arcsin (0.8)

Solve

\frac{180}{2} - x = π - arcsin (0.8) + 2 πn : x = - π + 90 - 2 πn + arcsin (0.8)

\frac{180}{2} - x = π - arcsin (0.8) + 2 πn

Divide the numbers:

\frac{180}{2} = 90

90 - x = π - arcsin (0.8) + 2 πn

Move

90

to the right side

90 - x = π - arcsin (0.8) + 2 πn

Subtract

90

from both sides

90 - x - 90 = π - arcsin (0.8) + 2 πn - 90

Simplify

- x = π - arcsin (0.8) + 2 πn - 90

- x = π - arcsin (0.8) + 2 πn - 90

Divide both sides by

- 1

- x = π - arcsin (0.8) + 2 πn - 90

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{π}{- 1} - \frac{arcsin ( 0.8 )}{- 1} + \frac{2 πn}{- 1} - \frac{90}{- 1}

Simplify

\frac{- x}{- 1} = \frac{π}{- 1} - \frac{arcsin ( 0.8 )}{- 1} + \frac{2 πn}{- 1} - \frac{90}{- 1}

Simplify

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Apply the fraction rule:

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

= \frac{x}{1}

Apply rule

\frac{a}{1} = a

= x

Simplify

\frac{π}{- 1} - \frac{arcsin ( 0.8 )}{- 1} + \frac{2 πn}{- 1} - \frac{90}{- 1} : - π + 90 - 2 πn + arcsin (0.8)

\frac{π}{- 1} - \frac{arcsin ( 0.8 )}{- 1} + \frac{2 πn}{- 1} - \frac{90}{- 1}

Group like terms

= \frac{π}{- 1} - \frac{90}{- 1} + \frac{2 πn}{- 1} - \frac{arcsin ( 0.8 )}{- 1}

\frac{π}{- 1} = - π

\frac{π}{- 1}

Apply the fraction rule:

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

= - \frac{π}{1}

Apply rule

\frac{a}{1} = a

= - π

= - π - \frac{90}{- 1} + \frac{2 πn}{- 1} - \frac{arcsin ( 0.8 )}{- 1}

\frac{90}{- 1} = - 90

\frac{90}{- 1}

Apply the fraction rule:

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

= - \frac{90}{1}

Apply rule

\frac{a}{1} = a

= - 90

\frac{2 πn}{- 1} = - 2 πn

\frac{2 πn}{- 1}

Apply the fraction rule:

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

= - \frac{2 πn}{1}

Apply rule

\frac{a}{1} = a

= - 2 πn

= - π - (- 90) - 2 πn - \frac{arcsin ( 0.8 )}{- 1}

Apply rule

- (- a) = a

= - π + 90 - 2 πn - \frac{arcsin ( 0.8 )}{- 1}

\frac{arcsin ( 0.8 )}{- 1} = - arcsin (0.8)

\frac{arcsin ( 0.8 )}{- 1}

Apply the fraction rule:

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

= - \frac{arcsin ( 0.8 )}{1}

Apply rule

\frac{a}{1} = a

= - arcsin (0.8)

= - π + 90 - 2 πn - (- arcsin (0.8))

Apply rule

- (- a) = a

= - π + 90 - 2 πn + arcsin (0.8)

x = - π + 90 - 2 πn + arcsin (0.8)

x = - π + 90 - 2 πn + arcsin (0.8)

x = - π + 90 - 2 πn + arcsin (0.8)

x = 90 - 2 πn - arcsin (0.8), x = - π + 90 - 2 πn + arcsin (0.8)

Show solutions in decimal form

x = 90 - 2 πn - 0.92729 \dots, x = - π + 90 - 2 πn + 0.92729 \dots

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Frequently Asked Questions (FAQ)

What is the general solution for sin(180/2-x)=0.8 ?
The general solution for sin(180/2-x)=0.8 is x=90-2pin-0.92729…,x=-pi+90-2pin+0.92729…