Find the positive and negative coterminal angles of 11π/3



To find the positive and negative coterminal angles of \( \frac{11\pi}{3} \), we follow these steps:

### Step 1: Find the reference angle
The first step is to reduce the given angle to a standard position between \( 0 \) and \( 2\pi \) by subtracting multiples of \( 2\pi \).

\[
\frac{11\pi}{3} - 2\pi \times n
\]

We know that \( 2\pi = \frac{6\pi}{3} \), so:

\[
\frac{11\pi}{3} - \frac{6\pi}{3} = \frac{5\pi}{3}
\]

The reference angle is \( \frac{5\pi}{3} \).

### Step 2: Find the positive coterminal angle
To find the positive coterminal angle, add \( 2\pi \) to \( \frac{5\pi}{3} \):

\[
\frac{5\pi}{3} + 2\pi = \frac{5\pi}{3} + \frac{6\pi}{3} = \frac{11\pi}{3}
\]

Since \( \frac{11\pi}{3} \) is already positive, we don't need to adjust further.

### Step 3: Find the negative coterminal angle
To find the negative coterminal angle, subtract \( 2\pi \) from \( \frac{11\pi}{3} \):

\[
\frac{11\pi}{3} - 2\pi = \frac{11\pi}{3} - \frac{6\pi}{3} = \frac{5\pi}{3}
\]

To make this negative, subtract another \( 2\pi \):

\[
\frac{5\pi}{3} - 2\pi = \frac{5\pi}{3} - \frac{6\pi}{3} = -\frac{\pi}{3}
\]

### Final Result:
- Positive coterminal angle: \( \frac{5\pi}{3} \)
- Negative coterminal angle: \( -\frac{\pi}{3} \)

Would you like more details or have any questions?

---

Here are some related questions you might be interested in:

1. What are coterminal angles?
2. How do you find the reference angle for a given angle?
3. How do coterminal angles relate to the unit circle?
4. Can you have more than two coterminal angles?
5. How do you find coterminal angles in degrees?

**Tip:** Coterminal angles differ by multiples of \( 2\pi \) (or 360°), so adding or subtracting \( 2\pi \) repeatedly gives new coterminal angles.

Learn how to find the positive and negative coterminal angles of 11π/3 using trigonometric principles. This detailed explanation covers the steps to determine coterminal angles and the concept of reference angles. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation