https://file.aiquickdraw.com/mathbot/file/1726054503047yxdiqz0x.jpg

To solve this problem, we need to determine how to represent the angle \(-330^\circ\) in standard position and then find one positive and one negative coterminal angle.

### Step 1: Drawing the Angle in Standard Position

An angle in standard position is measured counterclockwise from the positive \(x\)-axis. A negative angle means we measure clockwise from the positive \(x\)-axis.

- The angle \(-330^\circ\) means rotating 330 degrees clockwise.
- A full rotation is \(360^\circ\), so the equivalent positive angle can be calculated by adding \(360^\circ\) to \(-330^\circ\):
  \[
  360^\circ - 330^\circ = 30^\circ.
  \]
- Therefore, \(-330^\circ\) is coterminal with \(30^\circ\).

### Step 2: Finding Coterminal Angles

Coterminal angles are angles that share the same terminal side. To find coterminal angles, we add or subtract \(360^\circ\) from the given angle.

1. **Positive Coterminal Angle**:  
   Add \(360^\circ\) to \(-330^\circ\):
   \[
   -330^\circ + 360^\circ = 30^\circ.
   \]
   So, \(30^\circ\) is the positive coterminal angle.

2. **Negative Coterminal Angle**:  
   Subtract \(360^\circ\) from \(-330^\circ\):
   \[
   -330^\circ - 360^\circ = -690^\circ.
   \]
   So, \(-690^\circ\) is the negative coterminal angle.

### Summary

- **Positive Angle**: \(30^\circ\)
- **Negative Angle**: \(-690^\circ\)

Would you like more details or have any questions about this solution?

### Related Questions

1. What are coterminal angles, and how can we calculate them?
2. How do you convert between degrees and radians?
3. What is the significance of positive and negative angles in trigonometry?
4. How can you find the reference angle for a given angle?
5. How does the unit circle help in understanding trigonometric functions?

### Tip

When working with angles, always consider whether they are measured in degrees or radians, as this can affect how you calculate and interpret them!

Draw the following angle in standard position: -330°. Find one positive angle and one negative angle that is coterminal with the given angle.

Learn how to draw -330° in standard position and find coterminal angles. This trigonometry problem includes key concepts such as positive and negative angles, and formulas for coterminal angles, suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation