Question

Can someone explain to me why sin(2ϴ/3)= -1 has no solution. The question is "Exercises 25-38 involve equations with multiple angles. Solve each equation on the interval [0,2pi). Please ASAP. Thank you! :)

Answer 1

In the interval
`[0,2\pi)`, you have
`\sin x=-1` for
`x=\frac{3\pi}2`. Replacing
`x=\frac{2\theta}3`, you get


`\frac{2\theta}3=\frac{3\pi}2\implies\theta=\frac32*\frac{3\pi}2=\frac{9\pi}4`

But
`2\pi=\frac{8\pi}4<\frac{9\pi}4`, so that solution for
`\theta` falls outside the interval
`[0,2\pi)`.