Find the angle with least positive measure coterminal with -π/3

To find the angle with the least positive measure coterminal with \(-\frac{\pi}{3}\), follow these steps:

1. **Understand Coterminal Angles**: Coterminal angles differ by integer multiples of \(2\pi\). So, to find a coterminal angle, we can add or subtract \(2\pi\) to the given angle.

2. **Add \(2\pi\) to \(-\frac{\pi}{3}\)**:
   \[
   -\frac{\pi}{3} + 2\pi = -\frac{\pi}{3} + \frac{6\pi}{3} = \frac{5\pi}{3}
   \]

3. **Result**: The angle \(\frac{5\pi}{3}\) is the coterminal angle with the least positive measure.

So, the angle with the least positive measure coterminal with \(-\frac{\pi}{3}\) is \(\frac{5\pi}{3}\).

Would you like a detailed explanation, or do you have any questions?

Here are 5 related questions for practice:

1. What is the least positive coterminal angle with \(-\frac{\pi}{4}\)?
2. Find the coterminal angle between 0 and \(2\pi\) for \(-\frac{2\pi}{3}\).
3. Determine the coterminal angle between 0 and \(2\pi\) for \(4\pi\).
4. What is the angle between 0 and \(2\pi\) that is coterminal with \(-\frac{5\pi}{6}\)?
5. Find a negative coterminal angle for \(\frac{\pi}{3}\).

**Tip**: To find a positive coterminal angle, you can keep adding \(2\pi\) until the angle becomes positive.

Find the angle with least positive measure coterminal with -π/3.

Learn how to determine the least positive coterminal angle for -π/3 with a clear step-by-step guide. This problem involves key trigonometric concepts like coterminal angles and is suitable for high school students in Grades 10-12.

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