What is the general solution for -10sin(x)=-5sqrt(2) ?

The general solution for -10sin(x)=-5sqrt(2) is x= pi/4+2pin,x=(3pi)/4+2pin

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-10sin(x)=-5sqrt(2)

- 10 sin (x) = - 52

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

Degrees

x = 4 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n

Solution steps

- 10 sin (x) = - 52

Divide both sides by

- 10

- 10 sin (x) = - 52

Divide both sides by

- 10

\frac{- 10 sin ( x )}{- 10} = \frac{- 5 2}{- 10}

Simplify

\frac{- 10 sin ( x )}{- 10} = \frac{- 5 2}{- 10}

Simplify

\frac{- 10 sin ( x )}{- 10} : sin (x)

\frac{- 10 sin ( x )}{- 10}

Apply the fraction rule:

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

= \frac{10 sin ( x )}{10}

Divide the numbers:

\frac{10}{10} = 1

= sin (x)

Simplify

\frac{- 5 2}{- 10} : \frac{2}{2}

\frac{- 5 2}{- 10}

Apply the fraction rule:

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

= \frac{5 2}{10}

Cancel the common factor:

5

= \frac{2}{2}

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

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

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

General solutions for

sin (x) = \frac{2}{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{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( b )}{11}

y, \frac{sin ( 7 y )}{7} = \frac{cos ( 2 x )}{2} + \frac{1}{2}

3 cos (\frac{π x}{12}) + 8.4 = 7

sin (x) = \frac{1}{6}, tan (x)

2 sin^{2} (x) + sin (x) - 2 = 0

What is the general solution for -10sin(x)=-5sqrt(2) ?
The general solution for -10sin(x)=-5sqrt(2) is x= pi/4+2pin,x=(3pi)/4+2pin