The angle $$ \square $$ is coterminal to $$ \frac{13 \pi}{3} $$.

Question

UpStudy AI · Accepted Answer

To find an angle coterminal with $$ \frac{13\pi}{3} $$, we need to subtract multiples of $$ 2\pi $$ until the angle falls within the standard range of $$ [0, 2\pi) $$.

Here's the step-by-step process:

1. **Understand Coterminal Angles:**
   - Two angles are coterminal if they differ by an integer multiple of $$ 2\pi $$.

2. **Subtract $$ 2\pi $$ Multiples:**
   - Start with $$ \frac{13\pi}{3} $$.
   - Subtract $$ 2\pi $$ (which is $$ \frac{6\pi}{3} $$):
     $$
     \frac{13\pi}{3} - \frac{6\pi}{3} = \frac{7\pi}{3}
     $$
   - Subtract another $$ 2\pi $$ ($$ \frac{6\pi}{3} $$):
     $$
     \frac{7\pi}{3} - \frac{6\pi}{3} = \frac{\pi}{3}
     $$

3. **Result:**
   - The angle $$ \frac{\pi}{3} $$ is coterminal with $$ \frac{13\pi}{3} $$ and lies within the standard range $$ [0, 2\pi) $$.

**Final Answer:**
$$
\boxed{\dfrac{\pi}{3}}
$$
The angle $$ \frac{\pi}{3} $$ is coterminal with $$ \frac{13\pi}{3} $$.

The angle \( \square \) is coterminal to \( \frac{13 \pi}{3} \).

Real Tutor Solution

Answer

Solution

Mind Expander

Related Questions

Latest Trigonometry Questions