Question
1. The angle whose measure is \( -\frac{\pi}{9} \) radians would be equivalent to 2. The angle whose measure is \( \frac{2 \pi}{5} \) radians would be equivalent to
Ask by Huff Chambers. in the United States
Feb 24,2025
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Answer
1. \( -\frac{\pi}{9} \) radians is equivalent to \( -20^{\circ} \).
2. \( \frac{2\pi}{5} \) radians is equivalent to \( 72^{\circ} \).
Solution
Rewrite the angle by following steps:
- step0: Convert to degrees:
\(-\frac{\pi }{9}\)
- step1: Convert to degrees:
\(-20^{\circ}\)
Rewrite the number \( \frac{2\pi}{5} \).
Rewrite the angle by following steps:
- step0: Convert to degrees:
\(\frac{2\pi }{5}\)
- step1: Convert to degrees:
\(72^{\circ}\)
1. The angle whose measure is \( -\frac{\pi}{9} \) radians is equivalent to \( -20^{\circ} \).
2. The angle whose measure is \( \frac{2\pi}{5} \) radians is equivalent to \( 72^{\circ} \).
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Simplify this solution Bonus Knowledge
To find the equivalent angle for \( -\frac{\pi}{9} \), you can add \( 2\pi \) (a complete rotation) to it. So, \( -\frac{\pi}{9} + 2\pi = -\frac{\pi}{9} + \frac{18\pi}{9} = \frac{17\pi}{9} \). This means \( -\frac{\pi}{9} \) is equivalent to approximately \( 3.77 \) radians, which spins you almost a full circle clockwise! For the angle \( \frac{2\pi}{5} \), this is already a positive angle, but if you want to find its equivalent in degrees, just multiply by \( \frac{180}{\pi} \). Doing the math gives you \( \frac{2\pi}{5} \times \frac{180}{\pi} = 72 \) degrees. So, you can flaunt your angle as a sharp \( 72^\circ \)!
