Question

Arrange the angles in increasing order of their cosines.

3pie/4
pie
7pie/6
5pie/3
7pie/4
4pie/3
3pie/2
2pie

Answer 1

Explanation:

Answer 2

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

Explanation:

Convert each angle in degree measure:

`(3\pi)/(4)=135^(\circ),\\ \\\pi=180^(\circ),\\ \\(7\pi)/(6)=210^(\circ),\\ \\(5\pi)/(3)=300^(\circ),\\ \\(7\pi)/(4)=315^(\circ),\\ \\(4\pi)/(3)=240^(\circ),\\ \\(3\pi)/(2)=270^(\circ),\\ \\2\pi=360^(\circ).`

Then

`\cos (3\pi)/(4)=\cos 135^(\circ)=-(√(2))/(2),\\ \\\cos \pi=\cos 180^(\circ)=-1,\\ \\\cos (7\pi)/(6)=\cos 210^(\circ)=-(√(3))/(2),\\ \\\cos (5\pi)/(3)=\cos 300^(\circ)=(1)/(2),\\ \\\cos (7\pi)/(4)=\cos 315^(\circ)=(√(2))/(2),\\ \\\cos (4\pi)/(3)=\cos 240^(\circ)=-(1)/(2),\\ \\\cos (3\pi)/(2)=\cos 270^(\circ)=0,\\ \\\cos 2\pi=\cos 360^(\circ)=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.`