Question
Sketch the angle then find its reference angle 315^•
Answers
GPT-4o mini
To find the reference angle for \( 315^\circ \), you can follow these steps:
1. **Locate the angle**: \( 315^\circ \) is in the fourth quadrant of the unit circle.
2. **Determine the reference angle**: The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. For angles in the fourth quadrant, the reference angle can be found by subtracting the angle from \( 360^\circ \):
\[
\text{Reference Angle} = 360^\circ - 315^\circ = 45^\circ
\]
So, the reference angle for \( 315^\circ \) is \( 45^\circ \).
To sketch the angle:
- Draw a circle centered at the origin (0,0).
- Mark the positive x-axis as the starting position (0°).
- Rotate clockwise to \( 315^\circ \), which lands in the fourth quadrant.
- You should visualize the angle as being formed with the x-axis.
In summary:
- **Angle**: \( 315^\circ \)
- **Reference Angle**: \( 45^\circ \)
1. **Locate the angle**: \( 315^\circ \) is in the fourth quadrant of the unit circle.
2. **Determine the reference angle**: The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. For angles in the fourth quadrant, the reference angle can be found by subtracting the angle from \( 360^\circ \):
\[
\text{Reference Angle} = 360^\circ - 315^\circ = 45^\circ
\]
So, the reference angle for \( 315^\circ \) is \( 45^\circ \).
To sketch the angle:
- Draw a circle centered at the origin (0,0).
- Mark the positive x-axis as the starting position (0°).
- Rotate clockwise to \( 315^\circ \), which lands in the fourth quadrant.
- You should visualize the angle as being formed with the x-axis.
In summary:
- **Angle**: \( 315^\circ \)
- **Reference Angle**: \( 45^\circ \)