What is the general solution for sin((8pi)/(23))=sin(x) ?

The general solution for sin((8pi)/(23))=sin(x) is x=1.09272…+2pin,x=pi-1.09272…+2pin

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sin((8pi)/(23))=sin(x)

sin (\frac{8 π}{23}) = sin (x)

x = 1.09272 \dots + 2 πn, x = π - 1.09272 \dots + 2 πn

Degrees

x = 62.60869 \dots^{\circ} + 36 0^{\circ} n, x = 117.39130 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (\frac{8 π}{23}) = sin (x)

Switch sides

sin (x) = sin (\frac{8 π}{23})

Apply trig inverse properties

sin (x) = sin (\frac{8 π}{23})

General solutions for

sin (x) = sin (\frac{8 π}{23})

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

x = arcsin (sin (\frac{8 π}{23})) + 2 πn, x = π - arcsin (sin (\frac{8 π}{23})) + 2 πn

x = arcsin (sin (\frac{8 π}{23})) + 2 πn, x = π - arcsin (sin (\frac{8 π}{23})) + 2 πn

Show solutions in decimal form

x = 1.09272 \dots + 2 πn, x = π - 1.09272 \dots + 2 πn

- 2 sin (x) - 4 cos (2 x) = 0

sin (x) + 3 cos (x) = 0

cos (x) = \frac{1}{csc ( x )}

- cot (2 x) = 0

cos (x) = \frac{π}{6}

What is the general solution for sin((8pi)/(23))=sin(x) ?
The general solution for sin((8pi)/(23))=sin(x) is x=1.09272…+2pin,x=pi-1.09272…+2pin