other positive coterminal angles are 680°, 1040°... other negative coterminal angles are -40°, -400°, -760°... Also, you can simply add and subtract a number of revolutions, if all you need is any positive and negative coterminal angle. If you're wondering what the coterminal angle of some angle is, don't hesitate to use our tool - it's here to help you!



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For this example the angle is 2.5 radians.

1 decade ago.

Find Coterminal Angles - Trigonometry Calculator A calculator to find the exact value of a coterminal angle to a given trigonometric angle.

Now, check the results with our coterminal angle calculator - it displays the coterminal angle between 0 and 360° (or 0 and 2π), as well as some exemplary positive and negative coterminal angles.



For example, if α = 1400°, then the coterminal angle in the [0,360°) range is 320° - which is already one example of a positive coterminal angle. Subtract from .

A

In the figure above, drag A or D until this happens.



360 A

Why is this important?

Negative Coterminal Angle = Angle -360eval(ez_write_tag([[300,250],'calculator_academy-medrectangle-4','ezslot_9',107,'0','0']));eval(ez_write_tag([[300,250],'calculator_academy-medrectangle-4','ezslot_10',107,'0','1']));eval(ez_write_tag([[300,250],'calculator_academy-medrectangle-4','ezslot_11',107,'0','2'])); The formulas above would only yield one of each co terminal angles. The standard position means that one side of the angle is fixed along the positive x-axis, and the vertex is located at the origin.

305 If you drag AB around twice you find another coterminal angle and so on.

°



This gives you the least negative coterminal angle. (2pi)/3 Use unit circle: (16pi)/3 = (4pi)/3 + (12pi)/3 = (4pi)/3 + 4pi The arc (or angle) that is co-terminal to (4pi)/3 --> (4pi)/3 - 2pi = - (2pi)/3 If you want to find a few positive and negative coterminal angles, you need to subtract or add a number of complete circles. 330 Coterminal Angles are angles in standard position that have the same Initial Side and the same Terminal side. Find an angle that is positive, less than , and coterminal with .

Relevance. = Once this number is found, it must again get subtracted from the given angle 526 degrees.

What is a coterminal angle? One method is to find the coterminal angle in the [0,360°) range (or [0,2π) range), as we did in the previous paragraph (if your angle is already in that range, you don't need to do this step). Find the Reference Angle -(2pi)/3. ° Since the angle is in the fourth quadrant, subtract from .

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To find an angle coterminal to another you can do so by simply adding or subtracting any multiple of 360 degrees or 2 pi radians. Tap for more steps... To write as a fraction with a common denominator, multiply by . 7

+

°

3



Subtract from .

Coterminal(2pi/3) Enter angle in degrees or radians:-- Enter angle or number for inverse functions.

2pi/3... a full cycle is 2pi (360 degrees), so to find a coterminal angle, add 2pi or subtract 2pi to the angles you are given, so. Varsity Tutors © 2007 - 2020 All Rights Reserved, CDR Exam - Cardiovascular Disease Recertification Exam Test Prep, AFOQT - Air Force Officer Qualifying Test Test Prep, SAT Subject Test in Japanese with Listening Courses & Classes, CCNA Industrial - Cisco Certified Network Associate-Industrial Test Prep, ASE - National Institute for Automotive Service Excellence Training, CAPM - Certified Associate in Project Management Training, SE Exam - Professional Licensed Engineer Structural Engineering Exam Courses & Classes.

This number must then get subtracted from the 78 pi for the solution to be found. The resulting angle of is coterminal with but isn't positive. Otherwise,

First, divide one number by the other, rounding down (towards the floor): Then, multiply the divisor by the obtained number (called the quotient): Subtract this number from your initial number.

It turns out that angles that are coterminal have the same value for these functions.

Combine and . = Coterminal Angles Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side.For example 30 ° , − 330 ° and 390 ° are all coterminal.

It turns out that angles that are coterminal have the same value for these functions. Since the angle is in the fourth quadrant, subtract from .

First, you must convert the radians to degrees. or π

Favorite Answer. in standard position (angles with the initial side on the positive angles Find a positive and a negative angle coterminal with a The resulting angle of is positive, less than , and coterminal with . 55 This whole number must them be multiplied by 2 pi and subtracted from the given value.



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Coterminal Angle Calculator is a free online tool that displays the positive and negative coterminal angles for the given degree value. Coterminal angles Check out 39 similar 2d geometry calculators , What is a coterminal angle?



Repeat the step. The resulting angle of is positive, less than , and coterminal with .

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390 Now click the button “Calculate Coterminal Angle” to get the output, Finally, the positive and negative coterminal angles will be displayed in the output field. A coterminal angle is an angle that ends at the same location as another angle. What is the coterminal angle formula? In Mathematics, the coterminal angle is defined as an angle, where two angles are drawn in the standard position, also both have their terminal sides in the same location.

Tap for more steps... Subtract from .

305 For our previously chosen angle, α = 1400°, let's add and subtract 10 revolutions (or 100, why not): positive coterminal angle: β = α + 360 * 10 = 1400° + 3600° = 5000°, negative coterminal angle: β = α - 360 * 10 = 1400° - 3600° = -2200°. Do It Faster, Learn It Better. . How to find a coterminal angle between 0 and 360° (or 0 and 2π)?

= °

If two angles are drawn, they are coterminal if both their

Tap for more steps... To write as a fraction with a common denominator, multiply by . and subtract one --> -5pi/3.



eval(ez_write_tag([[580,400],'calculator_academy-medrectangle-3','ezslot_7',169,'0','0'])); Co-terminal angles are easy to calculator using the following formulas if in degrees. Also, you can remember the coterminal angles definition as angles that differ by a whole number of complete circles.

So the coterminal angles formula, β = α ± 360 * k, will look like this for our negative angle example: The same works for the [0,2π) range, all you need to change is the divisor - instead of 360, use 2π. If the angle is negative, keep adding 360 until the result is between 0 and +360. Here 405 is the positive coterminal angle, -315 is the negative coterminal angle. , If you play around with the multiples, you can figure out the angles you need.

-axis) that have a common terminal side. 4.9/5.0 Satisfaction Rating over the last 100,000 sessions.

Math Homework. The resulting angle of is coterminal with but isn't positive.

If told to find the least negative angle coterminal with 526 degrees, a similar calculation process would be used with the only difference being that the dividend of the given Angle and 360 degrees must be added up.

In other words, two angles are coterminal when the angles themselves are different, but their sides and vertices are identical. Simplify the result.

Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC. (In radians, 360° = 2π radians).

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degrees

are all coterminal. This coterminal angle calculator converts an angle in degrees or radians into two positive co-terminal angles, and two negative co-terminal angles. Then just add or subtract 360°, 720°, 1080°... (2π,4π,6π...), to obtain positive or negative coterminal angles to your given angle.

Combine fractions. Find an angle that is positive, less than , and coterminal with .

Remember that they are not the same thing - the reference angle is the angle between the terminal side of the angle and the x-axis, and it's always in the range of [0, 90] (or [0, π/2]).

55 Varsity Tutors does not have affiliation with universities mentioned on its website.

In the figure above, drag D around the origin counterclockwise so the angle is greater than 360°. π For example, 1 degrees and 361 degrees are at the same location since the total angles in a circle is 360 degrees.

− Coterminal angles definition, How to find coterminal angles? Coterminal angles formula.

5 But if, for some reason, you still prefer a list of exemplary coterminal angles (but we really don't understand why...), here you are: If you didn't find your query on that list, type the angle into our coterminal angle calculator - you'll get the answer in the blink of an eye! π

2 There are two methods that can be used to determine if two or more angles are coterminal. fsateacher.



− Keep going until angle DBC is coterminal with ABC. 1 radian is equal to 57.29 degrees so 2.5*57.28=114.59 degrees. π

The resulting angle of is positive, less than , and coterminal with . For example, one revolution for our exemplary α is not enough to have both a positive and negative coterminal angle - we'll get two positive ones, 1040° and 1760°.

Coterminal angles are those angles that share the terminal side of an angle occupying the standard position.

for each angle do the following: In trigonometry we use the functions of angles like sin, cos and tan. In this case, the smallest negative angle is needed meaning the dividend of 78 pi and 2 pi must get rounded up to the nearest whole number.

This number is 2.

° Simplify the result. It'd be awesome if you guys can work out both of these. For example, the coterminal angle of 45 is 405 and -315. The thing which can sometimes be confusing is the difference between the reference angle and coterminal angles definitions.
standard position as above, only the 3

Now drag point A around in the opposite direction π

One angle (DBC) has a measure of 72°, and the other (ABC) has a measure of 432°,


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