Question

Please help! Solve the equation on the interval [0,2pi)

Answer 1

`(5pi)/(6)`

Explanation:

Answer 2

`x = (\pi)/(6), (5 \pi)/(6)`

Explanation:

`\begin{aligned}3 \sin x & = \sin x + 1\\\implies 3 \sin x - \sin x & = 1\\2 \sin x & = 1\\\sin x & = (1)/(2)\\\implies x & = \sin^(-1)\left((1)/(2)\right)\\x & = (\pi)/(6) \pm 2 \pi n, (5 \pi)/(6)\pm 2 \pi n\end{aligned}`

Therefore, the value of x in the interval [0, 2π) is:

`x = (\pi)/(6), \frac{\boxed{5} \pi}{\boxed{6}}`