Question 122078
Start with the given set of equations 


*[Tex \LARGE r=2\sin\left(\theta\right)]


*[Tex \LARGE r=1]




*[Tex \LARGE 1=2\sin\left(\theta\right)] Plug in {{{r=1}}} into the first equation





*[Tex \LARGE \frac{1}{2}=\sin\left(\theta\right)] Divide both sides by 2




*[Tex \LARGE sin^{-1}\left(\frac{1}{2}\right)=\theta] Take the arcsine of both sides to isolate *[Tex \LARGE \theta]




*[Tex \LARGE \theta=\frac{\pi}{6}] or *[Tex \LARGE \theta=\frac{5\pi}{6}] Take the arcsine of {{{1/2}}} to get {{{pi/6}}} and {{{5pi/6}}}:







So because the answer format is *[Tex \LARGE \left(r,\theta\right)] this means we have the solutions: 



*[Tex \LARGE \left(1,\frac{\pi}{6}\right)] and *[Tex \LARGE \left(1,\frac{5\pi}{6}\right)] 



So the answer is D)



Note: Since the second equation is {{{r=1}}}, this means that the first coordinate (which is r) is also 1. So the answers will look like (1,?) and (1,?). So if you had no idea what to do, you could easily eliminate possible answers a) and b)