Question

Which of the following are in correct order from greatest to least? A pi/2,330degree,5pi/3,7pi/6,2pi/3 B 5pi/3,7pi/6,2pi/3,pi/2,330 C pi/2,2pi/3,7pi/6,5pi/3,330 D 330,5pi/3,7pi/6,2pi/3,pi/2

Answer 1

D) 330,
`(5\pi )/(3)`,
`(7\pi )/(6)`,
`(2\pi )/(3)`,
`(\pi )/(2)`

Explanation:

To find the order from greatest to least, we need to convert all
`\pi` terms to degrees.

We know that π = 180°

`(\pi )/(2) = (180)/(2) = 90`

`(5\pi )/(3) = (5*180)/(3) = (900)/(3) = 300`

`(7\pi )/(6) = (7*180)/(6) = (1260)/(6) = 210`

`(2\pi )/(3) = (2*180)/(3) = (360)/(3) = 120`

Now we have converted all in degrees. Let's arrange them from greatest to least.

330, 300, 210, 120, 90

Let's write them using
`\pi` term.

330,
`(5\pi )/(3)`,
`(7\pi )/(6)`,
`(2\pi )/(3)`,
`(\pi )/(2)`

Therefore, the answer is D) 330,
`(5\pi )/(3)`,
`(7\pi )/(6)`,
`(2\pi )/(3)`,
`(\pi )/(2)`

Answer 2

`330,(5\pi )/(3),(7\pi )/(6), (2\pi )/(3) ,(\pi )/(2)`

Explanation:

We have to find the alternate angles regarding π

So,

`(\pi )/(2) = 90 \\330\\(5\pi )/(3) = 300\\(7\pi )/(6) = 210\\(2\pi )/(3) = 120`

As we have all the angles in number form, we can sort them in descending order to get the answer

330, 300, 210, 120, 90

Writing using pi form

`330,(5\pi )/(3),(7\pi )/(6), (2\pi )/(3) ,(\pi )/(2)`

Hence, Option D is correct ..