What is the general solution for sin(x)=5sin(x)+2 ?

The general solution for sin(x)=5sin(x)+2 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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sin(x)=5sin(x)+2

sin (x) = 5 sin (x) + 2

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

Solution steps

sin (x) = 5 sin (x) + 2

Solve by substitution

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

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

Combine all the solutions

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

2 sin^{2} (x) + (3 - 4) sin (x) = 23

4 cos (30 x) + 12 = 10.5

3 sin^{2} (x) + 5 cos (x) = 1

1 + 4 sin (θ) = 0

2 sin (x) + cos (x) = - 2

What is the general solution for sin(x)=5sin(x)+2 ?
The general solution for sin(x)=5sin(x)+2 is x=(7pi)/6+2pin,x=(11pi)/6+2pin