Coterminal Angles: How to calculate coterminal angles, video lessons, examples and solutions
Many of your problems regarding coterminal angles can be solved with our co terminal angle calculator.
The angles that share the terminal side of the standard position are called coterminal angles.The standard position means that one side of the angle is fixed along the positive x- axis and the other side is located at the origin.
Two angles are coterminal when the angles themselves are not the same.
Coterminal angles are defined as angles that differ by a whole number of complete circles.Everything should be clear if you look at the picture below.
The coterminal angles start at the same side and share the terminal side.
There is a difference between the reference angle and coterminal angles definitions.The reference angle is between the terminal side of the angle and the x- axis, and it is always in the range of [0, /2].
If you are working in radians, you need to add or subtract a multiple to find the coterminal angles.Check to see if they agree with a coterminal angles formula.
Any two coterminal angles have the same trigonometric values.If they are coterminal, their sines, cosines and tangents are all equal.
All you need to do is to use a modulo operation and divide your angle by the 360 to determine the coterminal angle.
We will show you how it works with two examples.For a given angle, we want to find a coterminal angle with a measure of 0 and.
The coterminal angles formula will look like this for our negative angle example.
Check the results with our coterminal angle calculator, which displays the co terminal angle between 0 and 2, as well as some exemplary positive and negative co-terminal angles.
If you want to find a few positive and negative coterminal angles, you need to subtract or add a number of complete circles.How many?
If your angle is already in that range, you don't need to do this step.To get positive or negative coterminal angles to your given angle, just add or subtract.One example of a positive coterminal angle is if is 1400.
If you only need a positive and negative coterminal angle, you can simply add and subtract revolutions.Add and subtract 10 revolutions for our previously chosen angle.
When adding/subtracting, the number or revolutions must be large enough to change the sign.One revolution for our exemplary is not enough to have both a positive and negative coterminal angle.
Our tool can help you figure out what the coterminal angle of some angle is.
If, for some reason, you still prefer a list of exemplary coterminal angles, here you are.