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Popular >

15=-40sin(18(x-10))

Solution

15 = - 40 sin (18 (x - 10))

Solution

x = - \frac{0.38439 \dots}{18} + \frac{πn}{9} + 10, x = \frac{π + 0.38439 \dots}{18} + \frac{πn}{9} + 10

Degrees

x = 571.73422 \dots^{\circ} + 2 0^{\circ} n, x = 584.18136 \dots^{\circ} + 2 0^{\circ} n

Solution steps

15 = - 40 sin (18 (x - 10))

Switch sides

- 40 sin (18 (x - 10)) = 15

Divide both sides by

- 40

- 40 sin (18 (x - 10)) = 15

Divide both sides by

- 40

\frac{- 40 sin ( 18 ( x - 10 ) )}{- 40} = \frac{15}{- 40}

Simplify

\frac{- 40 sin ( 18 ( x - 10 ) )}{- 40} = \frac{15}{- 40}

Simplify

\frac{- 40 sin ( 18 ( x - 10 ) )}{- 40} : sin (18 (x - 10))

\frac{- 40 sin ( 18 ( x - 10 ) )}{- 40}

Apply the fraction rule:

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

= \frac{40 sin ( 18 ( x - 10 ) )}{40}

Divide the numbers:

\frac{40}{40} = 1

= sin (18 (x - 10))

Simplify

\frac{15}{- 40} : - \frac{3}{8}

\frac{15}{- 40}

Apply the fraction rule:

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

= - \frac{15}{40}

Cancel the common factor:

5

= - \frac{3}{8}

sin (18 (x - 10)) = - \frac{3}{8}

sin (18 (x - 10)) = - \frac{3}{8}

sin (18 (x - 10)) = - \frac{3}{8}

Apply trig inverse properties

sin (18 (x - 10)) = - \frac{3}{8}

General solutions for

sin (18 (x - 10)) = - \frac{3}{8}

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

18 (x - 10) = arcsin (- \frac{3}{8}) + 2 πn, 18 (x - 10) = π + arcsin (\frac{3}{8}) + 2 πn

18 (x - 10) = arcsin (- \frac{3}{8}) + 2 πn, 18 (x - 10) = π + arcsin (\frac{3}{8}) + 2 πn

Solve

18 (x - 10) = arcsin (- \frac{3}{8}) + 2 πn : x = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

18 (x - 10) = arcsin (- \frac{3}{8}) + 2 πn

Simplify

arcsin (- \frac{3}{8}) + 2 πn : - arcsin (\frac{3}{8}) + 2 πn

arcsin (- \frac{3}{8}) + 2 πn

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{3}{8}) = - arcsin (\frac{3}{8})

= - arcsin (\frac{3}{8}) + 2 πn

18 (x - 10) = - arcsin (\frac{3}{8}) + 2 πn

Divide both sides by

18

18 (x - 10) = - arcsin (\frac{3}{8}) + 2 πn

Divide both sides by

18

\frac{18 ( x - 10 )}{18} = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{2 πn}{18}

Simplify

x - 10 = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9}

x - 10 = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9}

Move

10

to the right side

x - 10 = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9}

Add

10

to both sides

x - 10 + 10 = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

Simplify

x = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

x = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

Solve

18 (x - 10) = π + arcsin (\frac{3}{8}) + 2 πn : x = \frac{π + arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

18 (x - 10) = π + arcsin (\frac{3}{8}) + 2 πn

Divide both sides by

18

18 (x - 10) = π + arcsin (\frac{3}{8}) + 2 πn

Divide both sides by

18

\frac{18 ( x - 10 )}{18} = \frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{2 πn}{18}

Simplify

x - 10 = \frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9}

x - 10 = \frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9}

Move

10

to the right side

x - 10 = \frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9}

Add

10

to both sides

x - 10 + 10 = \frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

Simplify

x - 10 + 10 = \frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

Simplify

x - 10 + 10 : x

x - 10 + 10

Add similar elements:

- 10 + 10 = 0

= x

Simplify

\frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10 : \frac{π + arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

\frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

Combine the fractions

\frac{π}{18} + \frac{arcsin ( \frac{3}{8} )}{18} : \frac{π + arcsin ( \frac{3}{8} )}{18}

Apply rule

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

= \frac{π + arcsin ( \frac{3}{8} )}{18}

= \frac{π + arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

x = \frac{π + arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

x = \frac{π + arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

x = \frac{π + arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

x = - \frac{arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10, x = \frac{π + arcsin ( \frac{3}{8} )}{18} + \frac{πn}{9} + 10

Show solutions in decimal form

x = - \frac{0.38439 \dots}{18} + \frac{πn}{9} + 10, x = \frac{π + 0.38439 \dots}{18} + \frac{πn}{9} + 10

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