Coterminal Angles: Negatives in Radians Explained

  • Thread starter Tyrion101
  • Start date
  • Tags
    Angles
In summary, the speaker is struggling with understanding coterminal angles, particularly when finding them for negative angles in radians. They mention possibly overthinking and not fully understanding negative angles, but acknowledge that they point in the opposite direction. They also provide an example of a negative angle (negative half pi) and its coterminal angle (three halves pi).
  • #1
Tyrion101
166
2
I've got my final test in trig coming up, and the one thing that I simply cannot get a handle on are, coterminal angles, specifically ones where you find coterminal angles for a negative angle, in my class they are mostly done in radians. I understand how to get all the angles of a positive radian, but not the negative. I think I am over thinking something here, it may just be that I don't exactly understand negative angles beyond the fact that you start the other way around. I hope this makes sense.
 
Mathematics news on Phys.org
  • #2
The rotated rays point in the same direction.

negative half pi is cotermianl with three halves pi.
 

1. What are coterminal angles?

Coterminal angles are angles that have the same initial and terminal sides, but differ in their measures by a multiple of 2π radians (or 360 degrees). In other words, they have the same starting and ending points on the unit circle, but can make multiple revolutions around the circle.

2. How do I find coterminal angles?

To find coterminal angles, simply add or subtract 2π radians (or 360 degrees) to the given angle. For example, if the given angle is 3π/4, its coterminal angles would be 3π/4 + 2π = 11π/4 and 3π/4 - 2π = -5π/4.

3. What is the significance of negative coterminal angles?

Negative coterminal angles occur when the angle is measured in a clockwise direction instead of the standard counterclockwise direction. In mathematics, we often use positive angles to represent counterclockwise rotations, but negative angles can also be used to represent clockwise rotations.

4. Why is it important to understand coterminal angles in radians?

Radians are a unit of measurement commonly used in mathematics and physics to measure angles based on the radius of a circle. Understanding coterminal angles in radians allows us to easily convert between degrees and radians, and to accurately measure and compare angles in different units.

5. How are coterminal angles useful in real life?

Coterminal angles are used in many real-life applications, such as navigation, engineering, and physics. For example, in navigation, coterminal angles can help us determine the direction and distance of a ship or plane. In engineering, coterminal angles are used to design and build structures, while in physics, they are used to describe and analyze rotational motion.

Similar threads

B Udemy Quiz Question on Radians and Quadrants
    • General Math
Replies
16
Views
1K
MHB Left or Right Angles ( + or - ) of adjoining vectors
    • General Math
Replies
2
Views
1K
How to Determine Correct Inverse Trig Angle?
    • Calculus and Beyond Homework Help
Replies
2
Views
105
B Why I think radians should *not* be dimensionless
    • General Math
Replies
10
Views
4K
Young's Photon Interference - Question on Angle & Voltage
    • Introductory Physics Homework Help
Replies
6
Views
826
MHB Find cos(x) and sin(x) if angle x has these properties....
    • General Math
Replies
1
Views
1K
MHB Finding a particular angle withion Johnson Solid J2
    • General Math
Replies
2
Views
2K
Efficient Calculation of Final Magnitude and Angle in Vector Addition Method
    • Electrical Engineering
Replies
33
Views
2K
B How to handle significant digits of exact values?
    • General Math
Replies
12
Views
2K
Are the angles of ∏/2 and 3∏/2 coterminal?
    • Precalculus Mathematics Homework Help
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top