What is the general solution for sin(x)=sin(pi/(10)) ?

The general solution for sin(x)=sin(pi/(10)) is x=0.31415…+2pin,x=pi-0.31415…+2pin

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sin(x)=sin(pi/(10))

sin (x) = sin (\frac{π}{10})

x = 0.31415 \dots + 2 πn, x = π - 0.31415 \dots + 2 πn

Solution steps

sin (x) = sin (\frac{π}{10})

sin (\frac{π}{10}) = \frac{2 3 - 5}{4}

sin (x) = \frac{2 3 - 5}{4}

Apply trig inverse properties

x = arcsin (\frac{2 3 - 5}{4}) + 2 πn, x = π - arcsin (\frac{2 3 - 5}{4}) + 2 πn

Show solutions in decimal form

x = 0.31415 \dots + 2 πn, x = π - 0.31415 \dots + 2 πn

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

sin (3 x) - sin (x) = - 2 sin (2 x) sin (x)

x, 0.05 cos (x) = - sin (x)

cos (x^{\circ}) = \frac{20.26}{26.4473}

cos (x) = \frac{- \frac{4}{3} 3}{\frac{8}{3} 3}

What is the general solution for sin(x)=sin(pi/(10)) ?
The general solution for sin(x)=sin(pi/(10)) is x=0.31415…+2pin,x=pi-0.31415…+2pin