Question

What are all the solutions for 4sintheta + 1 = 2sintheta from 0 to 2pi?

Would it be 7pi/6 and 11pi/6?

Answer 1

4 sin ( theta ) + 1 = 2 sin ( theta ) Subtract 2 sin ( theta to both sides )

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

2 sin ( theta ) + 1 = 0 Subtract 1 to both sides

2 sin ( theta ) + 1 - 1 = 0 - 1

2 sin ( theta ) = - 1 Divide both sides by 2

2 sin ( theta ) / 2 = - 1 / 2

sin ( theta ) = - 1 / 2

Your answer is correct.


theta = 7 pi / 6

and

theta = 11 pi / 6