To find the reference angle for \( 315^\circ \), you can follow these steps:
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Locate the angle: \( 315^\circ \) is in the fourth quadrant of the unit circle.
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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: \( 45^\circ \)