To find the **least positive coterminal angle** of a given angle, you can follow these steps:

### Step-by-Step Process:
1. **Identify the Given Angle**: Start with the angle you are given. Let's denote this angle as \(\theta\).
   
2. **Add/Subtract \(360^\circ\) or \(2\pi\)**: 
   - If \(\theta\) is in degrees, subtract or add \(360^\circ\) until you find a positive angle less than \(360^\circ\).
   - If \(\theta\) is in radians, subtract or add \(2\pi\) until you find a positive angle less than \(2\pi\) radians.

3. **Ensure the Result is Positive**: The final angle should be the smallest positive equivalent angle that lies within the standard interval for angles.

### Example Calculation:

- **Example 1**: Suppose \(\theta = 450^\circ\).
  - Subtract \(360^\circ\): \(450^\circ - 360^\circ = 90^\circ\).
  - The least positive coterminal angle is \(90^\circ\).

- **Example 2**: Suppose \(\theta = -45^\circ\).
  - Add \(360^\circ\): \(-45^\circ + 360^\circ = 315^\circ\).
  - The least positive coterminal angle is \(315^\circ\).

### Formula:
- **Degrees**: \(\theta + 360^\circ \times n\), where \(n\) is an integer.
- **Radians**: \(\theta + 2\pi \times n\), where \(n\) is an integer.

Would you like any further details or another example?

### Related Questions:
1. How do you find the least negative coterminal angle?
2. What is the general form of coterminal angles for any given angle?
3. How do you convert an angle from degrees to radians?
4. How do you determine if two angles are coterminal?
5. What are coterminal angles and how are they used in trigonometry?

**Tip**: Coterminal angles can be very useful when working with trigonometric functions, as they yield the same sine, cosine, and tangent values.

Discover how to find the least positive coterminal angle step-by-step with examples. This explanation covers trigonometric concepts and includes a formula for converting degrees to radians. Suitable for high school students learning trigonometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation