I find it hard to type the problem on the computer, so I included a picture with a note on where I am stuck. I know I can't divide "1" by "sin2theta" to get 30 degrees, so I don't know what to do next. Thanks.
I find it hard to type the problem on the computer, so I included a picture with a note on where I am stuck. I know I can't divide "1" by "sin2theta" to get 30 degrees, so I don't know what to do next. Thanks.
As you have written, $\displaystyle 0^\circ\leq2\theta<720^\circ\text.$ Where, in the interval $\displaystyle 0^\circ\leq\phi<720^\circ$, is $\displaystyle \sin\phi$ equal to 1? That would be $\displaystyle \phi = 90^\circ, 450^\circ\text.$ But in our case, the angle is $\displaystyle \phi = 2\theta\text.$ So
$\displaystyle 2\theta = 90^\circ\Rightarrow\theta = 45^\circ$
and
$\displaystyle 2\theta = 450^\circ\Rightarrow\theta = 225^\circ\text.$
If you substitute these back into the original equation, you'll see that the solution is $\displaystyle 45^\circ,$ and the second angle of $\displaystyle 225^\circ$ is an extraneous solution introduced when you squared both sides.