What is the general solution for 2sin(x)=4sin(x)+1 ?

The general solution for 2sin(x)=4sin(x)+1 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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2sin(x)=4sin(x)+1

2 sin (x) = 4 sin (x) + 1

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

Solution steps

2 sin (x) = 4 sin (x) + 1

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

- 1 - cos (θ) = - 3 cos (θ)

3 \cdot cos (θ) = 2 - sin (θ)

0.06 = 0.1 \cdot cos (4 x - 1.57)

tan (a) = \frac{20}{15}

sin (x) = - \frac{8}{8 13}

What is the general solution for 2sin(x)=4sin(x)+1 ?
The general solution for 2sin(x)=4sin(x)+1 is x=(7pi)/6+2pin,x=(11pi)/6+2pin