What is the general solution for sin((4pi)/(11))=sin(θ)*sin((7pi)/(11)) ?

The general solution for sin((4pi)/(11))=sin(θ)*sin((7pi)/(11)) is θ=1.57079…+2pin

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sin((4pi)/(11))=sin(θ)*sin((7pi)/(11))

sin (\frac{4 π}{11}) = sin (θ) \cdot sin (\frac{7 π}{11})

θ = 1.57079 \dots + 2 πn

Solution steps

sin (\frac{4 π}{11}) = sin (θ) sin (\frac{7 π}{11})

Switch sides

sin (θ) sin (\frac{7 π}{11}) = sin (\frac{4 π}{11})

Divide both sides by

sin (\frac{7 π}{11})

sin (θ) = \frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}

Apply trig inverse properties

θ = arcsin (\frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}) + 2 πn, θ = π - arcsin (\frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}) + 2 πn

Merge Overlapping Intervals

θ = arcsin (\frac{sin ( \frac{4 π}{11} )}{sin ( \frac{7 π}{11} )}) + 2 πn

Show solutions in decimal form

θ = 1.57079 \dots + 2 πn

sin (2 x) = 2 tan (2 x)

- 2 cos (2 θ) + 12 = 4 sin (θ) + 9

sec^{2} (x) + sec (x) - 2 = 0

(cot (x) - 1) (2 sin (x) + 1) = 0

y, x = tan (y)

What is the general solution for sin((4pi)/(11))=sin(θ)*sin((7pi)/(11)) ?
The general solution for sin((4pi)/(11))=sin(θ)*sin((7pi)/(11)) is θ=1.57079…+2pin