If you’ve just come across coterminal angles, and are wondering what they are and how you can calculate them, you’re in luck. In this post, we’re going to go over coterminal angles, as well as some other terms, to bring this topic closer to you.
What are coterminal angles?
Coterminal angles are two angles that share the same terminal side. If you look at a clock, you will notice that each hour has a name and the coterminal angle calculator can be found here.
For example, 30 degrees is coterminal with 330 degrees because they both share the same terminal side. Since these two angles are coterminal, their values are equal to one another. This means that if you know one of them, then any number used as an argument for this function will return the same result for both values.
Positive coterminal angles
Similar to positive numbers, positive coterminal angles are angles whose values are above 0. So, for example, if we have an angle of 45 degrees, its coterminal angles are 405 degrees and -315 degrees. Out of these two, the angle that is 405 degrees is the positive coterminal angle.
Radians are a unit of angle measure, typically used in trigonometry, that’s equal to 1 turn. A complete circle has a radius of 2π radians, or about 6.28 radians.
They represent the ratio of the length of an arc to its radius. The radian is defined as being equal to the angle subtended at the center of a circle by an arc whose length is equal to that of the circle’s radius.
The radian has been built into many math functions as a standard unit, but you may find it helpful to learn how it is calculated manually so that you can test your work or make sure you understand this concept before using it in other equations:
Degrees are used to measure angles in geometry. Degrees are also used to measure temperature, time, and angles in trigonometry. In astronomy, degrees are used to measure the declination of a star or planet (how far north or south it is).
Degrees can be shortened as either “°” or “deg” (or even just “o”).
Reference and coterminal angles
You can think of reference angle and coterminal angle as two sides of a triangle. In this case, the initial side is your reference angle, which is exactly what it sounds like: the initial position of your line or shape (and therefore its starting point). The second side is your coterminal angle. If you imagine adding a full rotation to an angle, then you’ll end up with a new starting point—and thus an entirely different line or shape!
How to use the coterminal angle calculator
The coterminal angle calculator has two modes. You can either:
- Find the coterminal angles of an angle you chose
- Check if two angles are coterminal
You can also choose either degrees or radians as your measurement.
Essentially, coterminal angles are one full circle apart from each other. So, if you’re calculating in degrees, the coterminal angles must be 360 degrees apart, and if you’re calculating in radians, the coterminal angles must be 2π radians apart.
With this in mind, you can check if two angles are coterminal in your head.
Coterminal angles are angles that have a common terminal side.
Coterminal angles are always 2π radians apart.
110 degrees, 470 degrees and 830 degrees are all positive coterminal angles