Question

Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.

Answer 1

We will have the following:

`\sin (2\theta)=-(1)/(2)\Rightarrow2\theta=2\pi n_1+(7\pi)/(6)`
`\Rightarrow\theta=\pi n_1+(7\pi)/(12)`

Now, we will solve for the following:

`\Rightarrow\pi n_1+(7\pi)/(12)\le2\pi\Rightarrow\pi n_1\le(17\pi)/(12)`
`\Rightarrow n_1\le(17)/(12)`

This value in degrees is:

`(17)/(12)\text{radians}=81.169\text{degrees}`

So, the solution is located in the interval:

`\lbrack0,81\rbrack`