Find all possible solutions for x in the interval [0,2π)

Question

6sinx - 1 =3sinx +1

Answer 1

When solving any trigonometric equation, you must bring all the trigonometric function to one side.

So,

6sin(x) - 1 = 3sin(x) + 1

6sin(x) - 3sin(x) - 1 = 1

Since 6 - 3 = 3, we have

3sin(x) - 1 = 1.

Next, let's isolate the sin(x) by adding 1 and dividing by 3.

3sin(x) = 2

sin(x) = 2/3

Lastly, use the inverse sine function (ie sin^-1 OR arcsin) to isolate x.

x = sin^-1(2/3)

Calculate the value using a calculator.

x ≈ 0.73 radians and (2π - 0.73) radians

*Please feel free to ask me any question for clarification.