find the angle theta in standard position with 0 degrees greater than or equal too theta greater than 360 degrees which corresponds to the bearing N 35 degrees W.
To find the angle theta in standard position that corresponds to the given bearing N 35 degrees W, we can follow these steps:
1. Start by understanding the bearing system:
- In the bearing system, the direction is given with respect to the north direction.
- The angles in the bearing system are measured clockwise from the north direction.
2. Determine the angle in standard position:
- In standard position, the initial side of the angle is the positive x-axis, while the terminal side is the line representing the given bearing.
- Since the bearing is N 35 degrees W, we need to find the angle between the positive x-axis and a line that is 35 degrees clockwise from the northern direction and is slanted towards the west.
3. Convert the bearing into an angle in standard position:
- Start from the north direction (0 degrees) and rotate 35 degrees clockwise to find the first point on the line.
- Then, rotate an additional 90 degrees clockwise to move from the north direction to the positive x-axis.
- Finally, continue rotating 35 degrees clockwise to reach the terminal side of the angle.
Let's calculate the angle theta:
- Start with 0 degrees (north direction) and rotate 35 degrees clockwise: 0 + 35 = 35 degrees.
- Rotate an additional 90 degrees clockwise: 35 + 90 = 125 degrees.
- Finally, rotate 35 degrees clockwise: 125 + 35 = 160 degrees.
Therefore, the angle theta in standard position that corresponds to the bearing N 35 degrees W is 160 degrees.