Question

Drag each tile to the correct box.Arrange the angles in increasing order of their cosines.

Answer 1

Given:

`\begin{gathered} (3\pi)/(4) \\ \pi \\ (7\pi)/(6) \\ (5\pi)/(3) \\ (7\pi)/(4) \\ (4\pi)/(3) \\ (3\pi)/(2) \\ 2\pi \end{gathered}`

To arrange the angles in increasing order, we first get the value of their cosines as shown below:

`cos(3\pi)/(4)=-(√(2))/(2)`
`cos\pi=-1`
`cos(7\pi)/(6)=-(√(3))/(2)`
`cos(5\pi)/(3)=(1)/(2)`
`cos(7\pi)/(4)=(√(2))/(2)`
`cos(4\pi)/(3)=-(1)/(2)`
`cos(3\pi)/(2)=0`
`cos2\pi=1`

Therefore, the angles in increasing order of their cosines are:

`\pi<(7\pi)/(6)<(3\pi)/(4)<(4\pi)/(3)<(3\pi)/(2)<(5\pi)/(3)<(7\pi)/(4)<2\pi`