drag each tile to the correct box. arrange the angles in increasing order of their cosines. $\frac{3pi}{4}$…

Explanation:

Step1: Recall cosine - values of angles

We know the unit - circle definitions of cosine. $\cos(\frac{3\pi}{4})=-\frac{\sqrt{2}}{2}\approx - 0.707$, $\cos(\pi)=-1$, $\cos(\frac{7\pi}{6})=-\frac{\sqrt{3}}{2}\approx - 0.866$, $\cos(\frac{5\pi}{3})=\frac{1}{2}=0.5$, $\cos(\frac{7\pi}{4})=\frac{\sqrt{2}}{2}\approx0.707$, $\cos(\frac{4\pi}{3})=-\frac{1}{2}=-0.5$, $\cos(\frac{3\pi}{2}) = 0$, $\cos(2\pi)=1$.

Step2: Arrange cosine - values in increasing order

$-1<-\frac{\sqrt{3}}{2}<-\frac{\sqrt{2}}{2}<-\frac{1}{2}<0<\frac{1}{2}<\frac{\sqrt{2}}{2}<1$.

Step3: Match angles with cosine - values

The angles in increasing order of their cosines are: $\pi<\frac{7\pi}{6}<\frac{3\pi}{4}<\frac{4\pi}{3}<\frac{3\pi}{2}<\frac{5\pi}{3}<\frac{7\pi}{4}<2\pi$.

Answer:

$\pi<\frac{7\pi}{6}<\frac{3\pi}{4}<\frac{4\pi}{3}<\frac{3\pi}{2}<\frac{5\pi}{3}<\frac{7\pi}{4}<2\pi$