What is the general solution for sin(0.6)-sin(0.6+x)=0.95 ?

The general solution for sin(0.6)-sin(0.6+x)=0.95 is x=-0.39559…+2pin-0.6,x=pi+0.39559…+2pin-0.6

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Popular >

sin(0.6)-sin(0.6+x)=0.95

Solution

sin (0.6) - sin (0.6 + x) = 0.95

Solution

x = - 0.39559 \dots + 2 πn - 0.6, x = π + 0.39559 \dots + 2 πn - 0.6

Degrees

x = - 57.04340 \dots^{\circ} + 36 0^{\circ} n, x = 168.28847 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (0.6) - sin (0.6 + x) = 0.95

sin (0.6) = sin (\frac{3}{5})

sin (0.6)

sin (\frac{3}{5}) - sin (0.6 + x) = 0.95

Move

sin (\frac{3}{5})

to the right side

sin (\frac{3}{5}) - sin (0.6 + x) = 0.95

Subtract

sin (\frac{3}{5})

from both sides

sin (\frac{3}{5}) - sin (0.6 + x) - sin (\frac{3}{5}) = 0.95 - sin (\frac{3}{5})

Simplify

- sin (0.6 + x) = 0.95 - sin (\frac{3}{5})

- sin (0.6 + x) = 0.95 - sin (\frac{3}{5})

Divide both sides by

- 1

- sin (0.6 + x) = 0.95 - sin (\frac{3}{5})

Divide both sides by

- 1

\frac{- sin ( 0.6 + x )}{- 1} = \frac{0.95}{- 1} - \frac{sin ( \frac{3}{5} )}{- 1}

Simplify

\frac{- sin ( 0.6 + x )}{- 1} = \frac{0.95}{- 1} - \frac{sin ( \frac{3}{5} )}{- 1}

Simplify

\frac{- sin ( 0.6 + x )}{- 1} : sin (0.6 + x)

\frac{- sin ( 0.6 + x )}{- 1}

Apply the fraction rule:

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

= \frac{sin ( 0.6 + x )}{1}

Apply rule

\frac{a}{1} = a

= sin (0.6 + x)

Simplify

\frac{0.95}{- 1} - \frac{sin ( \frac{3}{5} )}{- 1} : - 0.95 + sin (\frac{3}{5})

\frac{0.95}{- 1} - \frac{sin ( \frac{3}{5} )}{- 1}

Apply rule

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

= \frac{0.95 - sin ( \frac{3}{5} )}{- 1}

Apply the fraction rule:

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

= - \frac{0.95 - sin ( \frac{3}{5} )}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{0.95 - sin ( \frac{3}{5} )}{1} = 0.95 - sin (\frac{3}{5})

= - (0.95 - sin (\frac{3}{5}))

Distribute parentheses

= - (0.95) - (- sin (\frac{3}{5}))

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - 0.95 + sin (\frac{3}{5})

sin (0.6 + x) = - 0.95 + sin (\frac{3}{5})

sin (0.6 + x) = - 0.95 + sin (\frac{3}{5})

sin (0.6 + x) = - 0.95 + sin (\frac{3}{5})

Apply trig inverse properties

sin (0.6 + x) = - 0.95 + sin (\frac{3}{5})

General solutions for

sin (0.6 + x) = - 0.95 + sin (\frac{3}{5})

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

0.6 + x = arcsin (- 0.95 + sin (\frac{3}{5})) + 2 πn, 0.6 + x = π + arcsin (0.95 - sin (\frac{3}{5})) + 2 πn

0.6 + x = arcsin (- 0.95 + sin (\frac{3}{5})) + 2 πn, 0.6 + x = π + arcsin (0.95 - sin (\frac{3}{5})) + 2 πn

Solve

0.6 + x = arcsin (- 0.95 + sin (\frac{3}{5})) + 2 πn : x = arcsin (- 0.95 + sin (\frac{3}{5})) + 2 πn - 0.6

0.6 + x = arcsin (- 0.95 + sin (\frac{3}{5})) + 2 πn

Move

0.6

to the right side

0.6 + x = arcsin (- 0.95 + sin (\frac{3}{5})) + 2 πn

Subtract

0.6

from both sides

0.6 + x - 0.6 = arcsin (- 0.95 + sin (\frac{3}{5})) + 2 πn - 0.6

Simplify

x = arcsin (- 0.95 + sin (\frac{3}{5})) + 2 πn - 0.6

x = arcsin (- 0.95 + sin (\frac{3}{5})) + 2 πn - 0.6

Solve

0.6 + x = π + arcsin (0.95 - sin (\frac{3}{5})) + 2 πn : x = π + arcsin (0.95 - sin (\frac{3}{5})) + 2 πn - 0.6

0.6 + x = π + arcsin (0.95 - sin (\frac{3}{5})) + 2 πn

Move

0.6

to the right side

0.6 + x = π + arcsin (0.95 - sin (\frac{3}{5})) + 2 πn

Subtract

0.6

from both sides

0.6 + x - 0.6 = π + arcsin (0.95 - sin (\frac{3}{5})) + 2 πn - 0.6

Simplify

x = π + arcsin (0.95 - sin (\frac{3}{5})) + 2 πn - 0.6

x = π + arcsin (0.95 - sin (\frac{3}{5})) + 2 πn - 0.6

x = arcsin (- 0.95 + sin (\frac{3}{5})) + 2 πn - 0.6, x = π + arcsin (0.95 - sin (\frac{3}{5})) + 2 πn - 0.6

Show solutions in decimal form

x = - 0.39559 \dots + 2 πn - 0.6, x = π + 0.39559 \dots + 2 πn - 0.6

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Frequently Asked Questions (FAQ)

What is the general solution for sin(0.6)-sin(0.6+x)=0.95 ?
The general solution for sin(0.6)-sin(0.6+x)=0.95 is x=-0.39559…+2pin-0.6,x=pi+0.39559…+2pin-0.6