Find an angle between 0 and $$ 2 \pi $$ that is coterminal to $$ \frac{25 \pi}{6} $$.

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UpStudy AI · Accepted Answer

1. We start with the angle $$\frac{25\pi}{6}$$.

2. To find a coterminal angle between $$0$$ and $$2\pi$$, subtract multiples of $$2\pi$$ until the angle falls in the desired range. Recall that $$2\pi = \frac{12\pi}{6}$$.

3. First, subtract $$2\pi$$ once:
   $$
   \frac{25\pi}{6} - 2\pi = \frac{25\pi}{6} - \frac{12\pi}{6} = \frac{13\pi}{6}.
   $$
   Since $$\frac{13\pi}{6} > 2\pi$$ (because $$2\pi = \frac{12\pi}{6}$$), we need to subtract another $$2\pi$$.

4. Subtract $$2\pi$$ a second time:
   $$
   \frac{25\pi}{6} - 2(2\pi) = \frac{25\pi}{6} - \frac{24\pi}{6} = \frac{\pi}{6}.
   $$

5. The angle $$\frac{\pi}{6}$$ is between $$0$$ and $$2\pi$$.

Thus, an angle between $$0$$ and $$2\pi$$ that is coterminal to $$\frac{25\pi}{6}$$ is $$\frac{\pi}{6}$$.
An angle between $$0$$ and $$2\pi$$ that is coterminal to $$\frac{25\pi}{6}$$ is $$\frac{\pi}{6}$$.

Find an angle between 0 and that is coterminal to .

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