4 sin x =-1+2 sin x

Question

 solve the equation for  0≤ x < 2 pie

Answer 1

We need to isolate x like any algebraic equation:

 

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

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

2sin(x) = -1

sin(x) = -1/2

x = sin^-1(-1/2)

x = -.524

 

But since the answer must be between 0 and 2pi, you add 2pi to the answer to get it in the right range:

 

-.524 + 2pi = 5.759

 

 

Answer 2

4 Sin(x) = -1 +2 Sin(x)

 

[4 Sin(x)] - [2Sin(x)] = -1

 

(4-2) Sin(x) = -1

 

2 Sin(x) = -1

 

Sin(x) =  - 1/2

 

Can you take it from there?