What is the general solution for 15sin(x)+7=sin(x) ?

The general solution for 15sin(x)+7=sin(x) is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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15sin(x)+7=sin(x)

15 sin (x) + 7 = sin (x)

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

Solution steps

15 sin (x) + 7 = sin (x)

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

3 sin^{2} (x) + 2 sin (x) - 1 = 0

2 cos (θ) = 3

- 73 tan (θ) + 2 = 9

tan^{2} (x) + 2 sec (x) = - 1

2 cos^{2} (θ) + 3 cos (θ) + 1 = 0

What is the general solution for 15sin(x)+7=sin(x) ?
The general solution for 15sin(x)+7=sin(x) is x=(7pi)/6+2pin,x=(11pi)/6+2pin