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Popular >

solvefor x,-sin(0.6(x+y))*0.6+0.25=0

Solution

solve for

x, - sin (0.6 (x + y)) \cdot 0.6 + 0.25 = 0

Solution

x = \frac{0.42977 \dots + 2 πn}{0.6} - y, x = \frac{π - 0.42977 \dots + 2 πn}{0.6} - y

Solution steps

- sin (0.6 (x + y)) \cdot 0.6 + 0.25 = 0

Multiply both sides by

100

- sin (0.6 (x + y)) \cdot 0.6 + 0.25 = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

- sin (0.6 (x + y)) \cdot 0.6 \cdot 100 + 0.25 \cdot 100 = 0 \cdot 100

Refine

- 60 sin (0.6 (x + y)) + 25 = 0

- 60 sin (0.6 (x + y)) + 25 = 0

Move

25

to the right side

- 60 sin (0.6 (x + y)) + 25 = 0

Subtract

25

from both sides

- 60 sin (0.6 (x + y)) + 25 - 25 = 0 - 25

Simplify

- 60 sin (0.6 (x + y)) = - 25

- 60 sin (0.6 (x + y)) = - 25

Divide both sides by

- 60

- 60 sin (0.6 (x + y)) = - 25

Divide both sides by

- 60

\frac{- 60 sin ( 0.6 ( x + y ) )}{- 60} = \frac{- 25}{- 60}

Simplify

\frac{- 60 sin ( 0.6 ( x + y ) )}{- 60} = \frac{- 25}{- 60}

Simplify

\frac{- 60 sin ( 0.6 ( x + y ) )}{- 60} : sin (0.6 (x + y))

\frac{- 60 sin ( 0.6 ( x + y ) )}{- 60}

Apply the fraction rule:

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

= \frac{60 sin ( 0.6 ( x + y ) )}{60}

Divide the numbers:

\frac{60}{60} = 1

= sin (0.6 (x + y))

Simplify

\frac{- 25}{- 60} : \frac{5}{12}

\frac{- 25}{- 60}

Apply the fraction rule:

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

= \frac{25}{60}

Cancel the common factor:

5

= \frac{5}{12}

sin (0.6 (x + y)) = \frac{5}{12}

sin (0.6 (x + y)) = \frac{5}{12}

sin (0.6 (x + y)) = \frac{5}{12}

Apply trig inverse properties

sin (0.6 (x + y)) = \frac{5}{12}

General solutions for

sin (0.6 (x + y)) = \frac{5}{12}

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

0.6 (x + y) = arcsin (\frac{5}{12}) + 2 πn, 0.6 (x + y) = π - arcsin (\frac{5}{12}) + 2 πn

0.6 (x + y) = arcsin (\frac{5}{12}) + 2 πn, 0.6 (x + y) = π - arcsin (\frac{5}{12}) + 2 πn

Solve

0.6 (x + y) = arcsin (\frac{5}{12}) + 2 πn : x = \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

0.6 (x + y) = arcsin (\frac{5}{12}) + 2 πn

Divide both sides by

0.6

0.6 (x + y) = arcsin (\frac{5}{12}) + 2 πn

Divide both sides by

0.6

\frac{0.6 ( x + y )}{0.6} = \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

Simplify

x + y = \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

x + y = \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

Move

y

to the right side

x + y = \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

Subtract

y

from both sides

x + y - y = \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y

Simplify

x + y - y = \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y

Simplify

x + y - y : x

x + y - y

Add similar elements:

y - y = 0

= x

Simplify

\frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y : \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

\frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y

Combine the fractions

\frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} : \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6}

Apply rule

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

= \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6}

= \frac{2 πn + arcsin ( \frac{5}{12} )}{0.6} - y

= \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

x = \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

x = \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

x = \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

Solve

0.6 (x + y) = π - arcsin (\frac{5}{12}) + 2 πn : x = \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

0.6 (x + y) = π - arcsin (\frac{5}{12}) + 2 πn

Divide both sides by

0.6

0.6 (x + y) = π - arcsin (\frac{5}{12}) + 2 πn

Divide both sides by

0.6

\frac{0.6 ( x + y )}{0.6} = \frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

Simplify

x + y = \frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

x + y = \frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

Move

y

to the right side

x + y = \frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6}

Subtract

y

from both sides

x + y - y = \frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y

Simplify

x + y - y = \frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y

Simplify

x + y - y : x

x + y - y

Add similar elements:

y - y = 0

= x

Simplify

\frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y : \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

\frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} - y

Combine the fractions

\frac{π}{0.6} - \frac{arcsin ( \frac{5}{12} )}{0.6} + \frac{2 πn}{0.6} : \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6}

Apply rule

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

= \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6}

= \frac{π + 2 πn - arcsin ( \frac{5}{12} )}{0.6} - y

= \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

x = \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

x = \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

x = \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

x = \frac{arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y, x = \frac{π - arcsin ( \frac{5}{12} ) + 2 πn}{0.6} - y

Show solutions in decimal form

x = \frac{0.42977 \dots + 2 πn}{0.6} - y, x = \frac{π - 0.42977 \dots + 2 πn}{0.6} - y

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