Find the positive and negative coterminal angles of -9π/2



To find the positive and negative coterminal angles of \(-\frac{9\pi}{2}\), we follow a similar process as before.

### Step 1: Find the reference angle
First, let's reduce the given angle to a standard position between \(0\) and \(2\pi\) by adding multiples of \(2\pi\) (since the angle is negative).

\[
-\frac{9\pi}{2} + 2\pi \times n
\]

We know that \(2\pi = \frac{4\pi}{2}\), so:

\[
-\frac{9\pi}{2} + \frac{4\pi}{2} = -\frac{5\pi}{2}
\]

This is still negative, so add another \(2\pi\):

\[
-\frac{5\pi}{2} + \frac{4\pi}{2} = -\frac{\pi}{2}
\]

This is our reduced angle.

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

\[
-\frac{\pi}{2} + 2\pi = -\frac{\pi}{2} + \frac{4\pi}{2} = \frac{3\pi}{2}
\]

This is the positive coterminal angle.

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

\[
-\frac{\pi}{2} - 2\pi = -\frac{\pi}{2} - \frac{4\pi}{2} = -\frac{5\pi}{2}
\]

This is the negative coterminal angle.

### Final Result:
- Positive coterminal angle: \(\frac{3\pi}{2}\)
- Negative coterminal angle: \(-\frac{5\pi}{2}\)

Would you like more details or have any questions?

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Here are some related questions you might be interested in:

1. How do you find coterminal angles for angles greater than \(2\pi\)?
2. What is the difference between positive and negative angles on the unit circle?
3. How do you convert radians to degrees for coterminal angles?
4. How do you find the reference angle for an angle in radians?
5. Can coterminal angles be used to simplify trigonometric calculations?

**Tip:** When dealing with negative angles, you can always add \(2\pi\) repeatedly until you get a positive angle.

Learn how to find the positive and negative coterminal angles of -9π/2 radians using trigonometric principles. This problem involves reducing angles to standard positions and understanding coterminal angles in radians. Suitable for students in Grades 10-12.

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