Question

drag each tile to the correct box. arrange the angles in increasing order of their cosines. reset next 2π $\frac{3pi}{2}$ $\frac{4pi}{3}$ $\frac{7pi}{4}$ $\frac{5pi}{3}$ $\frac{7pi}{6}$ $pi$ $\frac{3pi}{4}$

Explanation:

Step1: Recall cosine - function properties

The cosine function \(y = \cos(x)\) has a period of \(2\pi\) and is symmetric about the \(y\) - axis (\(\cos(x)=\cos(-x)\)). Also, \(\cos(x)\) is decreasing on the interval \([0,\pi]\) and increasing on the interval \([\pi,2\pi]\).

Step2: Calculate cosine values

• \(\cos(2\pi)=1\)
• \(\cos(\frac{3\pi}{2}) = 0\)
• \(\cos(\frac{4\pi}{3})=-\frac{1}{2}\)
• \(\cos(\frac{7\pi}{4})=\frac{\sqrt{2}}{2}\)
• \(\cos(\frac{5\pi}{3})=\frac{1}{2}\)
• \(\cos(\frac{7\pi}{6})=-\frac{\sqrt{3}}{2}\)
• \(\cos(\pi)= - 1\)
• \(\cos(\frac{3\pi}{4})=-\frac{\sqrt{2}}{2}\)

Step3: Arrange in increasing order

Based on the calculated values, the order of the angles in increasing order of their cosines is: \(\pi,\frac{7\pi}{6},\frac{3\pi}{4},\frac{4\pi}{3},\frac{3\pi}{2},\frac{5\pi}{3},\frac{7\pi}{4},2\pi\)

Answer:

\(\pi,\frac{7\pi}{6},\frac{3\pi}{4},\frac{4\pi}{3},\frac{3\pi}{2},\frac{5\pi}{3},\frac{7\pi}{4},2\pi\)