What is the general solution for 3sin(C)-10=5sin(C)-9 ?

The general solution for 3sin(C)-10=5sin(C)-9 is C=(7pi)/6+2pin,C=(11pi)/6+2pin

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3sin(C)-10=5sin(C)-9

3 sin (C) - 10 = 5 sin (C) - 9

C = \frac{7 π}{6} + 2 πn, C = \frac{11 π}{6} + 2 πn

Solution steps

3 sin (C) - 10 = 5 sin (C) - 9

Solve by substitution

sin (C) = - \frac{1}{2}

sin (C) = - \frac{1}{2} : C = \frac{7 π}{6} + 2 πn, C = \frac{11 π}{6} + 2 πn

Combine all the solutions

C = \frac{7 π}{6} + 2 πn, C = \frac{11 π}{6} + 2 πn

23 sin (\frac{θ}{2}) = 3

tan (θ) = - \frac{1}{7}

2 sin (x) = \frac{4 cos ( x ) - 1}{tan ( x )}

6 cos (5 x) = 3

2 sin (2 θ) cos (θ) + cos (2 θ) sin (θ) = 0

What is the general solution for 3sin(C)-10=5sin(C)-9 ?
The general solution for 3sin(C)-10=5sin(C)-9 is C=(7pi)/6+2pin,C=(11pi)/6+2pin