sketch each angle in standard position draw an arrow representing the correct amount of of rotation l. Find the measure of two other angles one positive and one negative that are coternminal with given angle give the quadrant of each angle

To solve this problem, you will need to sketch angles in standard position, which means the initial side of each angle lies along the positive x-axis. The rotation from the initial side to the terminal side will be counterclockwise for positive angles and clockwise for negative angles.

### Step-by-Step Guide:

1. **Sketch the Given Angle in Standard Position:**
   - Begin by drawing a coordinate plane.
   - For the given angle, determine the correct amount of rotation from the positive x-axis. If the angle is positive, rotate counterclockwise; if negative, rotate clockwise.
   - Draw an arrow to indicate the direction of rotation, and place the terminal side in the appropriate quadrant.

2. **Identify Two Coterminal Angles:**
   - **Positive Coterminal Angle:** Add \(360^\circ\) (or \(2\pi\) radians) to the given angle.
   - **Negative Coterminal Angle:** Subtract \(360^\circ\) (or \(2\pi\) radians) from the given angle.
   - Both of these angles will share the same terminal side as the original angle.

3. **Determine the Quadrant:**
   - Based on the terminal side of the angle, determine the quadrant:
     - Quadrant I: \(0^\circ\) to \(90^\circ\)
     - Quadrant II: \(90^\circ\) to \(180^\circ\)
     - Quadrant III: \(180^\circ\) to \(270^\circ\)
     - Quadrant IV: \(270^\circ\) to \(360^\circ\)

### Example:

Let's say the given angle is \(135^\circ\):

1. **Sketch the Angle \(135^\circ\):**
   - Start at the positive x-axis.
   - Rotate \(135^\circ\) counterclockwise. This places the terminal side in Quadrant II.

2. **Find Two Coterminal Angles:**
   - Positive Coterminal Angle: \(135^\circ + 360^\circ = 495^\circ\)
   - Negative Coterminal Angle: \(135^\circ - 360^\circ = -225^\circ\)

3. **Determine the Quadrant:**
   - The original angle \(135^\circ\) is in Quadrant II.
   - The positive coterminal angle \(495^\circ\) (after subtracting \(360^\circ\)) is equivalent to \(135^\circ\), so it's also in Quadrant II.
   - The negative coterminal angle \(-225^\circ\) (after adding \(360^\circ\)) is equivalent to \(135^\circ\), so it also lies in Quadrant II.

### Questions:
1. How do you determine the quadrant of an angle if given in radians?
2. What is the process to convert between degrees and radians?
3. How would you sketch an angle greater than \(360^\circ\)?
4. What is the significance of coterminal angles in trigonometry?
5. How do coterminal angles help in simplifying trigonometric calculations?

### Tip:
When working with angles, always check whether they are in degrees or radians, as this will affect your calculations for coterminal angles and quadrant identification.

Learn how to sketch angles in standard position and find coterminal angles. Understand the concept of quadrants and how to determine them based on angle measurement. Detailed step-by-step guide with examples provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation