STANDARD POSITION
Definition Of Standard Position
Angle in standard position is an angle drawn on the x-y plane with its vertex at the origin and its initial side along the positive x-axis.
More About Standard Position
If the terminal side of an angle in standard position turns counterclockwise, then the angle is positive.
If the terminal side of an angle in standard position turns clockwise, then the angle is negative.
Video Examples:Angles in Standard Position
Example of Standard Position
- The figure below shows a positive angle.
Solved Example on Standard Position
Ques: A lighthouse makes an angle of 130° from ship due north as shown in the figure. Find the location of the lighthouse in terms of an angle in standard position.
Choices:
A. 230°
B. 320°
C. 310°
D. 130°
Correct Answer: B
Solution:
Step 1: The location of the lighthouse in terms of an angle in standard position is 360° - 40° = 320°.
Quick Summary
- Vertex at the origin.
- Initial side along the positive x-axis.
- Counterclockwise rotation is positive.
- Clockwise rotation is negative.
🍎 Teacher Insights
Use visual aids and interactive tools to demonstrate the concept of standard position. Emphasize the importance of the origin and positive x-axis as reference points.🎓 Prerequisites
- Coordinate plane
- Angles
- X and Y axes
Check Your Knowledge
Q1: An angle in standard position has its terminal side in the second quadrant. Which of the following could be the angle's measure?
Q2: Which of the following is NOT a characteristic of an angle in standard position?
Frequently Asked Questions
Q: What does standard position mean?
A: It is the convention of drawing angles with the vertex at the origin and the initial side along the positive x-axis.
Q: How to determine if the angle is positive or negative in standard position?
A: If the terminal side turns counterclockwise, then the angle is positive. If the terminal side turns clockwise, then the angle is negative.