What is the general solution for 2/(sin(x))+10=6 ?

The general solution for 2/(sin(x))+10=6 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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Popular >

2/(sin(x))+10=6

Solution

\frac{2}{sin ( x )} + 10 = 6

Solution

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Degrees

x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

\frac{2}{sin ( x )} + 10 = 6

Move

10

to the right side

\frac{2}{sin ( x )} + 10 = 6

Subtract

10

from both sides

\frac{2}{sin ( x )} + 10 - 10 = 6 - 10

Simplify

\frac{2}{sin ( x )} = - 4

\frac{2}{sin ( x )} = - 4

Multiply both sides by

sin (x)

\frac{2}{sin ( x )} = - 4

Multiply both sides by

sin (x)

\frac{2}{sin ( x )} sin (x) = - 4 sin (x)

Simplify

2 = - 4 sin (x)

2 = - 4 sin (x)

Switch sides

- 4 sin (x) = 2

Divide both sides by

- 4

- 4 sin (x) = 2

Divide both sides by

- 4

\frac{- 4 sin ( x )}{- 4} = \frac{2}{- 4}

Simplify

\frac{- 4 sin ( x )}{- 4} = \frac{2}{- 4}

Simplify

\frac{- 4 sin ( x )}{- 4} : sin (x)

\frac{- 4 sin ( x )}{- 4}

Apply the fraction rule:

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

= \frac{4 sin ( x )}{4}

Divide the numbers:

\frac{4}{4} = 1

= sin (x)

Simplify

\frac{2}{- 4} : - \frac{1}{2}

\frac{2}{- 4}

Apply the fraction rule:

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

= - \frac{2}{4}

Cancel the common factor:

2

= - \frac{1}{2}

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

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

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

Verify Solutions

Find undefined (singularity) points:

sin (x) = 0

Take the denominator(s) of

\frac{2}{sin ( x )} + 10

and compare to zero

sin (x) = 0

The following points are undefined

sin (x) = 0

Combine undefined points with solutions:

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

General solutions for

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

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 = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 2/(sin(x))+10=6 ?
The general solution for 2/(sin(x))+10=6 is x=(7pi)/6+2pin,x=(11pi)/6+2pin