Given:
Four series of angles are given.
To Find:
Identify the series with the correct order from greatest to least.
Solution:
the correct order from greatest to least is what is shown in the fourth option, i.e.,
[tex]330<\frac{5\pi}{3}<\frac{7\pi}{6}<\frac{2\pi}{3}<\frac{\pi}{2}[/tex]
Calculation:
Now, we use the fact that
[tex]\pi =180[/tex]
to calculate the values of
[tex]\frac{\pi}{2}, \frac{2\pi}{3}, \frac{7\pi}{6}, \frac{5\pi}{3}[/tex]
So, we have
[tex]\frac{\pi}{2} = 90\\\\\frac{2\pi} {3}=\frac{(2)(180)}{3} = 120\\\\ \frac{7\pi} {6}=\frac{(7)(180)}{6} = 210\\\\ \frac{5\pi} {3}=\frac{(5)(180)}{3} = 300\\\\[/tex]
Looking at the above values, we see that the correct order from greatest to least is what is shown in the fourth option, i.e.,
[tex]330<\frac{5\pi}{3}<\frac{7\pi}{6}<\frac{2\pi}{3}<\frac{\pi}{2}[/tex]
Answer:
Option 4. is the correct option.
Step-by-step explanation:
The given angles are π/2, 330°,5π/3, 7π/6, 2π/3.
we have to arrange these angle in decreasing order.
First we will convert these angles from radian to degree.
π/2 = 90°
5π/3 = 5×180/3 = 300°
7π/6 = 7×180/6 = 210°
2π/3 = 2×180/3 = 120°
and 330°
Now the decreasing order of the angles is
330°, 300°, 210°, 120°, 90°
Therefore 330°, 5π/3, 7π/6, 2π/3, π/2 is the correct answer.
