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Popular >

5sin(62.83x)=-0.32

Solution

5 sin (62.83 x) = - 0.32

Solution

x = - \frac{0.06404 \dots}{62.83} + \frac{2 πn}{62.83}, x = \frac{π}{62.83} + \frac{0.06404 \dots}{62.83} + \frac{2 πn}{62.83}

+1

Degrees

x = - 0.05840 \dots^{\circ} + 5.72974 \dots^{\circ} n, x = 2.92327 \dots^{\circ} + 5.72974 \dots^{\circ} n

Solution steps

5 sin (62.83 x) = - 0.32

Divide both sides by

5

5 sin (62.83 x) = - 0.32

Divide both sides by

5

\frac{5 sin ( 62.83 x )}{5} = \frac{- 0.32}{5}

Simplify

\frac{5 sin ( 62.83 x )}{5} = \frac{- 0.32}{5}

Simplify

\frac{5 sin ( 62.83 x )}{5} : sin (62.83 x)

\frac{5 sin ( 62.83 x )}{5}

Divide the numbers:

\frac{5}{5} = 1

= sin (62.83 x)

Simplify

\frac{- 0.32}{5} : - 0.064

\frac{- 0.32}{5}

Apply the fraction rule:

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

= - \frac{0.32}{5}

Divide the numbers:

\frac{0.32}{5} = 0.064

= - 0.064

sin (62.83 x) = - 0.064

sin (62.83 x) = - 0.064

sin (62.83 x) = - 0.064

Apply trig inverse properties

sin (62.83 x) = - 0.064

General solutions for

sin (62.83 x) = - 0.064

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

62.83 x = arcsin (- 0.064) + 2 πn, 62.83 x = π + arcsin (0.064) + 2 πn

62.83 x = arcsin (- 0.064) + 2 πn, 62.83 x = π + arcsin (0.064) + 2 πn

Solve

62.83 x = arcsin (- 0.064) + 2 πn : x = - \frac{arcsin ( \frac{8}{125} )}{62.83} + \frac{2 πn}{62.83}

62.83 x = arcsin (- 0.064) + 2 πn

Simplify

arcsin (- 0.064) + 2 πn : - arcsin (\frac{8}{125}) + 2 πn

arcsin (- 0.064) + 2 πn

arcsin (- 0.064) = - arcsin (\frac{8}{125})

arcsin (- 0.064)

= arcsin (- \frac{8}{125})

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{8}{125}) = - arcsin (\frac{8}{125})

= - arcsin (\frac{8}{125})

= - arcsin (\frac{8}{125}) + 2 πn

62.83 x = - arcsin (\frac{8}{125}) + 2 πn

Divide both sides by

62.83

62.83 x = - arcsin (\frac{8}{125}) + 2 πn

Divide both sides by

62.83

\frac{62.83 x}{62.83} = - \frac{arcsin ( \frac{8}{125} )}{62.83} + \frac{2 πn}{62.83}

Simplify

x = - \frac{arcsin ( \frac{8}{125} )}{62.83} + \frac{2 πn}{62.83}

x = - \frac{arcsin ( \frac{8}{125} )}{62.83} + \frac{2 πn}{62.83}

Solve

62.83 x = π + arcsin (0.064) + 2 πn : x = \frac{π}{62.83} + \frac{arcsin ( 0.064 )}{62.83} + \frac{2 πn}{62.83}

62.83 x = π + arcsin (0.064) + 2 πn

Divide both sides by

62.83

62.83 x = π + arcsin (0.064) + 2 πn

Divide both sides by

62.83

\frac{62.83 x}{62.83} = \frac{π}{62.83} + \frac{arcsin ( 0.064 )}{62.83} + \frac{2 πn}{62.83}

Simplify

x = \frac{π}{62.83} + \frac{arcsin ( 0.064 )}{62.83} + \frac{2 πn}{62.83}

x = \frac{π}{62.83} + \frac{arcsin ( 0.064 )}{62.83} + \frac{2 πn}{62.83}

x = - \frac{arcsin ( \frac{8}{125} )}{62.83} + \frac{2 πn}{62.83}, x = \frac{π}{62.83} + \frac{arcsin ( 0.064 )}{62.83} + \frac{2 πn}{62.83}

Show solutions in decimal form

x = - \frac{0.06404 \dots}{62.83} + \frac{2 πn}{62.83}, x = \frac{π}{62.83} + \frac{0.06404 \dots}{62.83} + \frac{2 πn}{62.83}

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