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Popular Trigonometry >

8sin((3.14)/(4*x))=7

Solution

8 sin (\frac{3.14}{4 \cdot x}) = 7

Solution

x = \frac{3.14}{4 ( 1.06543 \dots + 2 πn )}, x = \frac{3.14}{4 ( π - 1.06543 \dots + 2 πn )}

Degrees

x = 0^{\circ} + 6.12049 \dots^{\circ} n, x = 0^{\circ} + 5.38046 \dots^{\circ} n

Solution steps

8 sin (\frac{3.14}{4 x}) = 7

Divide both sides by

8

8 sin (\frac{3.14}{4 x}) = 7

Divide both sides by

8

\frac{8 sin ( \frac{3.14}{4 x} )}{8} = \frac{7}{8}

Simplify

sin (\frac{3.14}{4 x}) = \frac{7}{8}

sin (\frac{3.14}{4 x}) = \frac{7}{8}

Apply trig inverse properties

sin (\frac{3.14}{4 x}) = \frac{7}{8}

General solutions for

sin (\frac{3.14}{4 x}) = \frac{7}{8}

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

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn, \frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn, \frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn

Solve

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn : x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn

Multiply both sides by

x

\frac{3.14}{4 x} = arcsin (\frac{7}{8}) + 2 πn

Multiply both sides by

x

\frac{3.14}{4 x} x = arcsin (\frac{7}{8}) x + 2 πn x

Simplify

\frac{3.14}{4} = arcsin (\frac{7}{8}) x + 2 πn x

\frac{3.14}{4} = arcsin (\frac{7}{8}) x + 2 πn x

Switch sides

arcsin (\frac{7}{8}) x + 2 πn x = \frac{3.14}{4}

Factor

arcsin (\frac{7}{8}) x + 2 πn x : x (arcsin (\frac{7}{8}) + 2 πn)

arcsin (\frac{7}{8}) x + 2 πn x

Factor out common term

x

= x (arcsin (\frac{7}{8}) + 2 πn)

x (arcsin (\frac{7}{8}) + 2 πn) = \frac{3.14}{4}

Divide both sides by

arcsin (\frac{7}{8}) + 2 πn; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

x (arcsin (\frac{7}{8}) + 2 πn) = \frac{3.14}{4}

Divide both sides by

arcsin (\frac{7}{8}) + 2 πn; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

\frac{x ( arcsin ( \frac{7}{8} ) + 2 πn )}{arcsin ( \frac{7}{8} ) + 2 πn} = \frac{\frac{3.14}{4}}{arcsin ( \frac{7}{8} ) + 2 πn}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

Simplify

\frac{x ( arcsin ( \frac{7}{8} ) + 2 πn )}{arcsin ( \frac{7}{8} ) + 2 πn} = \frac{\frac{3.14}{4}}{arcsin ( \frac{7}{8} ) + 2 πn}

Simplify

\frac{x ( arcsin ( \frac{7}{8} ) + 2 πn )}{arcsin ( \frac{7}{8} ) + 2 πn} : x

\frac{x ( arcsin ( \frac{7}{8} ) + 2 πn )}{arcsin ( \frac{7}{8} ) + 2 πn}

Cancel the common factor:

arcsin (\frac{7}{8}) + 2 πn

= x

Simplify

\frac{\frac{3.14}{4}}{arcsin ( \frac{7}{8} ) + 2 πn} : \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}

\frac{\frac{3.14}{4}}{arcsin ( \frac{7}{8} ) + 2 πn}

Apply the fraction rule:

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

= \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}

x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = - \frac{arcsin ( \frac{7}{8} )}{2 π}

Solve

\frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn : x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

\frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn

Multiply both sides by

x

\frac{3.14}{4 x} = π - arcsin (\frac{7}{8}) + 2 πn

Multiply both sides by

x

\frac{3.14}{4 x} x = π x - arcsin (\frac{7}{8}) x + 2 πn x

Simplify

\frac{3.14}{4} = π x - arcsin (\frac{7}{8}) x + 2 πn x

\frac{3.14}{4} = π x - arcsin (\frac{7}{8}) x + 2 πn x

Switch sides

π x - arcsin (\frac{7}{8}) x + 2 πn x = \frac{3.14}{4}

Factor

π x - arcsin (\frac{7}{8}) x + 2 πn x : x (π - arcsin (\frac{7}{8}) + 2 πn)

π x - arcsin (\frac{7}{8}) x + 2 πn x

Factor out common term

x

= x (π - arcsin (\frac{7}{8}) + 2 πn)

x (π - arcsin (\frac{7}{8}) + 2 πn) = \frac{3.14}{4}

Divide both sides by

π - arcsin (\frac{7}{8}) + 2 πn; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

x (π - arcsin (\frac{7}{8}) + 2 πn) = \frac{3.14}{4}

Divide both sides by

π - arcsin (\frac{7}{8}) + 2 πn; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

\frac{x ( π - arcsin ( \frac{7}{8} ) + 2 πn )}{π - arcsin ( \frac{7}{8} ) + 2 πn} = \frac{\frac{3.14}{4}}{π - arcsin ( \frac{7}{8} ) + 2 πn}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

Simplify

\frac{x ( π - arcsin ( \frac{7}{8} ) + 2 πn )}{π - arcsin ( \frac{7}{8} ) + 2 πn} = \frac{\frac{3.14}{4}}{π - arcsin ( \frac{7}{8} ) + 2 πn}

Simplify

\frac{x ( π - arcsin ( \frac{7}{8} ) + 2 πn )}{π - arcsin ( \frac{7}{8} ) + 2 πn} : x

\frac{x ( π - arcsin ( \frac{7}{8} ) + 2 πn )}{π - arcsin ( \frac{7}{8} ) + 2 πn}

Cancel the common factor:

π - arcsin (\frac{7}{8}) + 2 πn

= x

Simplify

\frac{\frac{3.14}{4}}{π - arcsin ( \frac{7}{8} ) + 2 πn} : \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}

\frac{\frac{3.14}{4}}{π - arcsin ( \frac{7}{8} ) + 2 πn}

Apply the fraction rule:

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

= \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}

x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}; n \neq = \frac{- π + arcsin ( \frac{7}{8} )}{2 π}

x = \frac{3.14}{4 ( arcsin ( \frac{7}{8} ) + 2 πn )}, x = \frac{3.14}{4 ( π - arcsin ( \frac{7}{8} ) + 2 πn )}

Show solutions in decimal form

x = \frac{3.14}{4 ( 1.06543 \dots + 2 πn )}, x = \frac{3.14}{4 ( π - 1.06543 \dots + 2 πn )}

Graph

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