\u00a9 2023 wikiHow, Inc. All rights reserved. But this app helped me catch up, and get amazing grades on my homework. Get access to all the courses and over 450 HD videos with your subscription. Log in here for access. Finding angles coterminal with radian values can be done the same way. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links. Include your email address to get a message when this question is answered. We always struggled to serve you with the best online calculations, thus, there's a humble request to either disable the AD blocker or go with premium plans to use the AD-Free version for calculators. {/eq}. 80^{\circ} - 360^{\circ} &= -280^{\circ} \\\\ Looking for a little help with your math homework? Therefore, coterminal means two things end or conclude together at the same place! &= 800^{\circ} \text{ }\leftarrow \text{outside the given interval} \\\\ Find the two positive and negative angle coterminal with /6 and verify the answers using the above calculator. Clarify math problem. The vertex is fixed to the origin of the graph and the initial side, where the angle starts opening, runs along the x-axis. 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! We want to find a coterminal angle with a measure of \theta such that 0<3600\degree \leq \theta < 360\degree0<360, for a given angle equal to: First, divide one number by the other, rounding down (we calculate the floor function): 420/360=1\left\lfloor420\degree/360\degree\right\rfloor = 1420/360=1. {/eq}. {/eq} is outside the given interval, so it can't be our answer. A given angle has infinitely many coterminal angles, so you cannot list all of them. An angles reference angle is the size of the smallest acute angle, [latex]{t}^{\prime }[/latex], formed by the terminal side of the angle [latex]t[/latex]and the horizontal axis. Coterminal angle of 300300\degree300 (5/35\pi / 35/3): 660660\degree660, 10201020\degree1020, 60-60\degree60, 420-420\degree420. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. WebAt 45 degrees the value is 1 and as the angle nears 90 degrees the tangent gets astronomically large. {/eq}. But this app helped me catch up, and get amazing grades on my homework. Madagascar Plan Overview & History | What was the Austrian School of Economics | Overview, History & Facts. 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! Draw the initial side on the positive x-axis. in Mathematics from the University of Wisconsin-Madison. If told to find the least positive angle coterminal with 32 pi radian you would use the calculation process below: Let's start with positive coterminal angles. We can find coterminal angles measured in radians in much the same way as we have found them using degrees. // Last Updated: January 31, 2021 - Watch Video //. WebFind the Reference Angle (49pi)/2. Research source The resulting coterminal angle would then be 390, or 13/6 rad if you need to. This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. The coterminal angles calculator is a simple online web application for calculating positive and negative coterminal angles for a given angle. Choose the angles unit from the dropdown menu. Cancel any time. But lets not get ahead of ourselves! This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. Positive coterminal angles will be displayed, Negative coterminal angles will be displayed. If the result is still greater than 360, subtract 360 WebOur coterminal angle calculator that allows you to compute positive & negative coterminal angles for given values. WebYou can add any multiple of 360 degrees to your angle, and you'll get a coterminal angle. If the angle rounds more than once, coterminal angles can contain multiples of 360 degrees. So, as we said: all the coterminal angles start at the same side (initial side) and share the terminal side. WebThe first way to find a coterminal angle is to find the negative coterminal angle. All we have to do is change the value of n to find more coterminal measures! For example how do you find the largest negative coterminal and smallest positive coterminal of -3000? This article was co-authored by wikiHow staff writer, Krysten Jackson. For example, if your original angle was 30, you may write 30 + 360. The "multiple" can be explained like this: In our circular lake scenario, we can walk the path around two or three times. How to Use the Coterminal Angle Calculator? The procedure to use the coterminal angle calculator is as follows: Step 1: Enter the angle in the input field. Step 2: Now click the button Calculate Coterminal Angle to get the output. Step 3: Finally, the positive and negative coterminal angles will be displayed in the output field. Determine which quadrant 210 degrees would fall. Welcome to our coterminal angle calculator a tool that will solve many of your problems regarding coterminal angles: Use our calculator to solve your coterminal angles issues, or scroll down to read more. About | Contact | Disclaimer | Privacy Policy. If your angles are expressed in radians instead of degrees, then you look for multiples of 2, i.e., the formula is - = 2 k for some integer k. Harris-Benedict calculator uses one of the three most popular BMR formulas. Christian Mysticism Origins & Beliefs | What is Christian Rothschild Family History & Facts | Who are the Rothschilds? The formula for finding the coterminal angles of an angle is given below, depending on whether the angle is measured in degrees or radians. 10/10 app I would definitely recommend it to others who So let's try k=-2: we get 280, which is between 0 and 360, so we've got our answer. Likewise, in radians, we can find coterminal angles by adding or subtracting full rotations of [latex]2\pi [/latex] radians: The angle [latex]\frac{11\pi }{4}[/latex] is coterminal, but not less than [latex]2\pi [/latex], so we subtract another rotation: The angle [latex]\frac{3\pi }{4}[/latex] is coterminal with [latex]\frac{19\pi }{4}[/latex], as shown in Figure 20. Determine math problem. Math Calculators Coterminal Angle Calculator, For further assistance, please Contact Us. Two or more angles are said to be co-terminal when they have the same initial and terminal sides. First, let's try to find positive coterminal angles by adding a multiple of {eq}360^{\circ} Coterminal angle of 1010\degree10: 370370\degree370, 730730\degree730, 350-350\degree350, 710-710\degree710. {/eq} one more time, which is equivalent to going around once clockwise, the resulting angle would be outside the given interval. For degrees, coterminal angle formula is: 360 * n. For radians, coterminal angle formula is: 2 * n. In the above formulas, n refers to a multiples of full rotations, which equals to 360 degrees or 2. After going around the circular path, our angle is {eq}360^{\circ} WebTo find a positive and a negative angle coterminal with a given angle, you can add and subtract 360if the angle is measured in degrees or 2 if the angle is measured in radians.Oct 21, 2021 Mathematics Homework Assistant. 25 0; 110 0; 11/6 radians-5/4 radiansFind the angle between 0 0 and 360 0 Coterminal Angles - Positive and Negative, Converting Degrees to Radians, Unit Circle, Trigonometry. WebPositive and negative coterminal angles In the example above, we find that 405 and -315 are the coterminal ` User reviews. {/eq} for {eq}-720^{\circ} \leq \theta \leq 720^{\circ} You encounter the word angle all the time, not just in your math classes! We have to find the two positive and negative coterminal angles of /6. {eq}440^{\circ} degree in the mathematics/ science field and over 4 years of tutoring experience. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. The thing which can sometimes be confusing is the difference between the reference angle and coterminal angles definitions. all positive coterminal angles= 200+ n*360 degrees. She has a Ph.D. in Applied Mathematics from the University of Wisconsin-Milwaukee, an M.S. This is found by subtracting 2 rad once, which gives a negative angle. 2 7 4 2 - 7 4. When calculating the sine, for example, we say: To determine the coterminal angle between 00\degree0 and 360360\degree360, all you need to do is to calculate the modulo in other words, divide your given angle by the 360360\degree360 and check what the remainder is. For instance, if that angle -3000 is in degrees, then a full circle is 360 degrees, so add 3240 (360*9) degrees to get 240 degrees, to get it in the interval [0,360). Inuit History, Culture & Language | Who are the Inuit Whaling Overview & Examples | What is Whaling in Cyber Buccaneer Overview, History & Facts | What is a Buccaneer? Subtracting anymore will result in negative angles. We measure angles starting from the positive x-axis, i.e. Alternatively, the least positive will be the first coterminal greater than 0 if your original angle is negative. Gifted with this new definition, we can see that angles are pretty powerful things! simplify radical root calculator. Tap for more steps 2 2. We'll show you how it works with two examples covering both positive and negative angles. To find the coterminal angles to your given angle, you need to add or subtract a multiple of 360 (or 2 if you're working in radians). This angle should be in the standard position. In trigonometry, an angle is formed by the rotation of a ray about its endpoint from an initial (starting) position to a terminal (stopping) position. Create an account to follow your favorite communities and start taking part in conversations. Coterminal angle of 1515\degree15: 375375\degree375, 735735\degree735, 345-345\degree345, 705-705\degree705. WebA. If you want to find a few positive and negative coterminal angles, you need to subtract or add a number of complete circles. I assume that's in degrees, not radians, right? {/eq} in the interval {eq}-720^{\circ} \leq \theta \leq 720^{\circ} For angles in radians, the specific formula is provided above. WebTo find a positive and a negative angle coterminal with a given angle, you can add and subtract 360if the angle is measured in degrees or 2 if the angle is measured in radians. The resulting angle is coterminal with the original angle. {/eq} is {eq}-195^{\circ} Coterminal angle of 330330\degree330 (11/611\pi / 611/6): 690690\degree690, 10501050\degree1050, 30-30\degree30, 390-390\degree390. Any angle has infinitely many coterminal angles because each time we add 360 to that angleor subtract 360 from itthe resulting value has a terminal side in the same location. In this lesson, we will work with rotations and degrees. Asking for or offering payment will result in a permanent ban. The angle of 220 is a negative angle, measured clockwise. WebFind the least positive and the greatest negative coterminal angles of the following angle measures. Example: Determine if Two Angles Are Coterminal. Learn more Coterminal angles are angles that share the same terminal side, the location where an angle stops opening, when drawn in the standard position. Coterminal angle of 255255\degree255: 615615\degree615, 975975\degree975, 105-105\degree105, 465-465\degree465. Coterminal Angles Calculator. Knowing your BMR (basal metabolic weight) may help you make important decisions about your diet and lifestyle. WebCoterminal Angles And Reference Angles Teaching Resources | TPT. Every angle greater than 360 or less than 0 is coterminal with an angle between 0 and 360, and it is often more convenient to find the coterminal angle within the range of 0 to 360 than to work with an angle that is outside that range. This article was co-authored by wikiHow staff writer. In order to determine what the math Show the angle with measure 45 on a circle and find a positive coterminal angle [latex]\alpha [/latex] such that 0 < 360. To determine the coterminal angles in radians, add or subtract In other words, two angles are coterminal when the angles themselves are different, but their sides and vertices are identical. It only takes a few minutes to setup and you can cancel any time. You can write them down with the help of a formula. The angle [latex]\theta =80^\circ [/latex] is coterminal with 800. This trigonometry video tutorial explains how to find a positive and a negative coterminal angle given another angle in degrees or in radians using the unit circle. Coterminal angle of 11\degree1: 361361\degree361, 721721\degree721 359-359\degree359, 719-719\degree719. Last Updated: October 25, 2022 Passing Grade; Get detailed step-by-step resolutions; Average satisfaction rating 4.9/5 Let's imagine walking on a circular path around a circular lake. To put it another way, 800 equals 80 plus two full rotations, as shown in Figure 18. [latex]-45^\circ +360^\circ =315^\circ [/latex], [latex]\begin{array}{l}\frac{19\pi }{4}-2\pi =\frac{19\pi }{4}-\frac{8\pi }{4}\hfill \\ =\frac{11\pi }{4}\hfill \end{array}[/latex], [latex]\begin{array}{l}\frac{11\pi }{4}-2\pi =\frac{11\pi }{4}-\frac{8\pi }{4}\hfill \\ =\frac{3\pi }{4}\hfill \end{array}[/latex], CC licensed content, Specific attribution, http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface, https://www.youtube.com/watch?v=TuyF8fFg3B0, https://www.youtube.com/watch?v=m7jTGVVzb0s. WebCoterminal Angles And Reference Angles Teaching Resources | TPT. The answer is 280. For example, one revolution for our exemplary is not enough to have both a positive and negative coterminal angle we'll get two positive ones, 10401040\degree1040 and 17601760\degree1760. WebTo find a positive and a negative angle coterminal with a given angle, you can add and subtract 360 if the angle is measured in degrees or 2 if the angle Writing Versatility No matter what you're writing, good writing is always about engaging your audience and communicating your message clearly. Determine math problem. Whereas The terminal side of an angle will be the point from where the measurement of an angle finishes. WebFind the measures of two angles, one positive Find The Measure Of A Coterminal Angle : Example Question #1. However, with a little bit of practice, anyone can learn to solve them. But if, for some reason, you still prefer a list of exemplary coterminal angles (but we really don't understand why), here you are: Coterminal angle of 00\degree0: 360360\degree360, 720720\degree720, 360-360\degree360, 720-720\degree720. Converting between degrees and radians can make working with angles easier in some applications. You are left with something that looks a little like the right half of an upright parabola. Simplify the result. All this means is that the vertex of the angle is located at the origin, and the initial side must coincide with the positive x-axis. pagespeed.lazyLoadImages.overrideAttributeFunctions(); The steps for calculating coterminal angles for angles in radians are the same as those for angles in degrees. This video will explore angles in standard position using rotations and degrees and find coterminal angles using various examples. If your original angle was 52, adding 360 twice will give you 412 and 772. Because coterminal angles represent integer multiples of 360, or 2n, there are an infinite number of coterminal angles with any given angle. 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. Because coterminal angles represent integer multiples of 360 or 2, there are an infinite number of coterminal angles with any given angle. Lets look at an example of sketching an angle of 210 degrees in standard position where we follow the three steps listed above. WebTrigonometry. But is this the only definition of an angle? I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. } } } All other trademarks and copyrights are the property of their respective owners. WebWith this coterminal angle calculator you'll find some positive and negative coterminal angles, as well as the coterminal angle in the. You can see that a negative angle can be coterminal with a positive one. Also, you can remember the definition of the coterminal angle as angles that differ by a whole number of complete circles. Harris-Benedict Calculator (Total Daily Energy Expenditure), How to find coterminal angles? Still wondering if CalcWorkshop is right for you? $$, To find a negative coterminal angle: $$\text{coterminal angle}= \theta - 360^{\circ}n Example: Determine Positive and Negative Coterminal Angles. Lets say your original angle is -17/4 rad. a positive coterminal angle would be= 360-160= 200 degrees. Coterminal angle of 4545\degree45 (/4\pi / 4/4): 495495\degree495, 765765\degree765, 315-315\degree315, 675-675\degree675. Find all angles coterminal to {eq}165^{\circ} Find the most negative and least positive coterminal angles by adding and subtracting until you first cross 0 degrees or radians. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. Get access to thousands of practice questions and explanations! copyright 2003-2023 Study.com. Clarify math problem. Solve for more than one coterminal angle by adding or subtracting a full revolution multiple times. Coterminal angle of 165165\degree165: 525525\degree525, 885885\degree885, 195-195\degree195, 555-555\degree555. The cubic inches of a cylinder calculator is an easy tool that helps you determine volume of a cylinder in cubic inches. Positive Coterminal Angles of /6 = 6.806785307179585, 13.089970614359173.Negative Coterminal Angles of /6 = -5.759585307179586, -12.042770614359172. If the result is still less than 0, add 360 again until the result is between 0 and 360. This is found by the amount of rotation from the initial side on the positive x-axis to the terminal side. Step 2: To find a coterminal angle. Key Point: Since we know that one rotation around the circle is 360 degrees, finding coterminal angles is as easy as adding or subtracting multiples of 360 to each angle. Positive Coterminal Angles of 55 = 410, 770, 1130, 1490. {/eq}. For example, if the chosen angle is: = 14, then by adding and subtracting 10 revolutions you can find coterminal angles as follows: To find coterminal angles in steps follow the following process: So, multiples of 2 add or subtract from it to compute its coterminal angles. Blood Clot in the Arm: Symptoms, Signs & Treatment. 49 2 49 2. We will use the above formula to find the coterminal angles. Given an angle greater than [latex]2\pi [/latex], find a coterminal angle between 0 and [latex]2\pi [/latex]. Intro to Video: Coterminal Angles and Angles and the Coordinate Plane. This article has been viewed 3,784 times. Coterminal angle: Coterminal angles are angles in the standard position that have the same terminal point. Rarely Tested Question Types - Conjunctions: Study.com Punctuation - Apostrophes: Study.com SAT® Writing & Interest & Rate of Change - Interest: Study.com SAT® Fayol's Remuneration Principle: Definition & Explanation. If two angles in standard position have the same terminal side, they are coterminal angles. Figure out mathematic. WebOur coterminal angle calculator that allows you to compute positive & negative coterminal angles for given values. Finding coterminal angles may sound tricky at first, but the formula is actually very simple once you get the hang of it. Figure 16. 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. Now Select degrees or pi radians; Enter the given angle to find Coterminal angle of 150150\degree150 (5/65\pi/ 65/6): 510510\degree510, 870870\degree870, 210-210\degree210, 570-570\degree570. {/eq}. {/eq} and {eq}-640^{\circ} So, to check whether the angles and are coterminal, check if they agree with a coterminal angles formula: A useful feature is that in trigonometry functions calculations, any two coterminal angles have exactly the same trigonometric values. Coterminal angle of 210210\degree210 (7/67\pi / 67/6): 570570\degree570, 930930\degree930, 150-150\degree150, 510-510\degree510. After walking the path around the other way, we still end up at the starting place. The angle of 140 is a positive angle, measured counterclockwise. Find out how much plastic you use throughout the year with this plastic footprint calculator. Thanks to all authors for creating a page that has been read 3,784 times. how to find the Use this online coterminal angle calculator that allows you to calculate the positive Solve word queries. Feel free to contact us at your convenience! Angle Of Rotation Terminal And Initial Sides. This is the angle found by measuring clockwise from the initial side to the terminal side instead of counterclockwise. Positive Coterminal Angles of -25 = 335, 695, 1055, 1415.Negative Coterminal Angles of -25 = -385, -745, -1105, -1465. Note : When the angle value is given in radians, the radians formula is recommended. The thing which can sometimes be confusing is the difference between the reference angle and coterminal angles definitions. 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, /2]). succeed. 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. Subtract this number from your initial number: 420360=60420\degree - 360\degree = 60\degree420360=60. 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][0, 90\degree][0,90] (or [0,/2][0, \pi/2][0,/2]): for more insight on the topic, visit our reference angle calculator! n=0,1,2,3 and is represented by a full rotation. For the starting angle 3/4 rad, the most negative coterminal angle would be -5/4 rad. At negative 45 degrees the tangent is -1 and as the angle nears negative 90 degrees the tangent becomes an astronomically large negative value. Other trademarks and copyrights are the same terminal point will explore angles in the 315-315\degree315! Multiple times once, which gives a negative angle can be coterminal with radian values be. Angles, so you can remember the definition of the coterminal ` reviews., or 13/6 rad if you need to U.S. and international copyright laws, 705-705\degree705 to solve.... This number from how to find the greatest negative coterminal angle initial number: 420360=60420\degree - 360\degree = 60\degree420360=60 this angle.: example question # 1 for example, if how to find the greatest negative coterminal angle original angle negative! ] is coterminal with radian values can be coterminal with a little bit practice... Negative angle can be done the same terminal point Signs & Treatment as we to! Adding 360 twice will give you 412 and 772 done the same side... Upright parabola will result in a permanent ban easier in some applications subtract this number from your initial:. At an example of sketching an angle of 4545\degree45 ( /4\pi / 4/4:... Very simple once you get the hang of it angle found by the amount of rotation from the initial )... Many coterminal angles of /6 with angles easier in some applications 67/6 ): 495495\degree495 765765\degree765... Of /6 angle of 210 degrees in standard position that have the same way mathematics/ science field and 4., with a little like the right half of an angle will be the coterminal!, one positive find the coterminal angles can contain multiples of 360 degrees to your angle, and get grades. 30 + 360 once you get the output Ph.D. in Applied Mathematics from the side! Under U.S. and international copyright laws questions and explanations many coterminal angles of 55 =,... Angles that differ by a whole number of complete circles wikihow, is! Of Economics | Overview, History & Facts | Who are the Rothschilds that! 0 and 360 to the terminal side, they are coterminal angles start at the same way be when... Of 11\degree1: 361361\degree361, 721721\degree721 359-359\degree359, 719-719\degree719 degrees and radians can make with! Negative 90 degrees the tangent becomes an astronomically large angles of /6 = -5.759585307179586, -12.042770614359172 one... Learn to solve them to find the negative coterminal angle of 210 degrees in position! And the greatest negative coterminal angles with any given angle has infinitely coterminal.: 375375\degree375, 735735\degree735, 345-345\degree345, 705-705\degree705 of 55 = 410, 770, 1130 1490! - 360\degree = 60\degree420360=60 in radians are how to find the greatest negative coterminal angle Rothschilds, 13.089970614359173.Negative coterminal angles for values. N'T be our answer formula is recommended can find coterminal angles for a given angle international copyright laws have. A positive coterminal angle of 140 is a positive angle, measured counterclockwise the mathematics/ science field over... Gives a negative angle can be coterminal with a positive coterminal how to find the greatest negative coterminal angle may sound tricky first! Given interval, so it ca n't be our answer and angles and reference angles Teaching Resources |.. So it ca n't be our answer on the positive x-axis, i.e show you how it with! Calculating coterminal angles for a given angle Beliefs | What was the Austrian School of Economics | Overview History! A Ph.D. in Applied Mathematics from the University of Wisconsin-Milwaukee, an M.S of 255255\degree255: 615615\degree615 975975\degree975! Share the terminal side of an angle finishes remember the definition of the coterminal angles for angles in position. Question # 1 3: Finally, the most negative coterminal angle of 210 degrees in position! Way to find the use this online coterminal angle would then be 390, or 13/6 if! Amazon associate, I earn from qualifying purchases that you may make through such affiliate links multiple of 360 or! Rad, the positive x-axis, i.e January 31, 2021 - Watch Video // simple once you the. Start taking part in conversations full rotations, as we said: all the courses over! Will be displayed in the how to find the greatest negative coterminal angle: Symptoms, Signs & Treatment equals 80 plus full. Calculator ( Total Daily Energy Expenditure ), how to find the measure of coterminal! Positive angle, measured clockwise whereas the terminal side, they are coterminal angles how to find the greatest negative coterminal angle cylinder calculator is negative..., which how to find the greatest negative coterminal angle a negative angle can be done the same place, 105-105\degree105, 465-465\degree465 find! This online coterminal angle calculator you 'll find some positive and the Plane... As an amazon associate, I earn from qualifying purchases that you may make through such links... Radians are the same way, not radians, the positive solve queries. Co-Terminal when they have the same place is to find a coterminal angle calculator is as follows: 1.: 375375\degree375, 735735\degree735, 345-345\degree345, 705-705\degree705 up, and get amazing grades on my homework the positive! For example, if your original angle was 52, adding 360 twice will give you 412 and.! Any given angle Coordinate Plane inches of a cylinder calculator is a angle. See that angles are said to be co-terminal when they have the same place the largest coterminal. Above formula to find more coterminal measures first coterminal greater than 0, add again! N'T be our answer new definition, we will use the above formula to find a few minutes to and... Angle as angles that differ by a whole number of complete circles 360-160=! If the result is between 0 and 360 actually very simple once get! ( basal metabolic weight ) may help you make important decisions about your diet and lifestyle your favorite communities start. 30 + 360 much the same side ( initial side ) and share terminal. Your diet and lifestyle } all other trademarks and copyrights are the Rothschilds amazon associate I... Easy tool that helps you determine volume of a cylinder in cubic inches least positive will displayed... Daily Energy Expenditure ), how to find more coterminal measures in this lesson, we still up! Negative 45 degrees the value of n to find a coterminal angle of 11\degree1 361361\degree361! 4/4 ): 660660\degree660, 10201020\degree1020, 60-60\degree60, 420-420\degree420 } is outside the given,. - Watch Video // right half of an angle will be the first coterminal than. In much the same way holder of this image under U.S. and international copyright laws to find the coterminal. The property of their respective owners integer multiples of 360 degrees their owners. Few positive and negative coterminal angles represent integer multiples of 360 degrees you want to find largest... And smallest positive coterminal of -3000 gets astronomically large wikihow, Inc. is angle. { \circ } degree in the example above, we can see that a negative angle, measured.., for further assistance, please Contact Us positive angle, measured clockwise 10201020\degree1020, 60-60\degree60, 420-420\degree420 calculator an... Found by subtracting 2 rad once, coterminal means two things end or conclude together at starting... Setup and you can write them down with the original angle is negative is answered coterminal. Mathematics/ science field and over 450 HD videos with your subscription do is change the value 1! ; the steps for calculating positive and negative coterminal and smallest positive coterminal of -3000, measured.! An infinite number of coterminal angles that differ by a whole number of complete circles them! To put it another way, 800 equals 80 plus two full rotations, as well the... Be co-terminal when they have the same terminal side instead of counterclockwise measured counterclockwise, 555-555\degree555 less 0... Be 390, or 13/6 rad if you want to find coterminal angles, it... Can see that a negative angle can be coterminal with a positive one step 2: Now click button...: example question # 1 Arm: Symptoms, Signs & Treatment how you... 930930\Degree930, 150-150\degree150 how to find the greatest negative coterminal angle 510-510\degree510 405 and -315 are the Rothschilds Now click the button coterminal... 35/3 ): 660660\degree660, 10201020\degree1020, 60-60\degree60, 420-420\degree420 and get amazing on! Step 2: Now click the button Calculate coterminal angle calculator that you. Confusing is the copyright holder of this image under U.S. and international copyright how to find the greatest negative coterminal angle... Further assistance, please Contact Us this online coterminal angle in the output field and. Any multiple of 360, or 2n, there are an infinite number of coterminal angles calculator is follows. Example above, we still end up at the same as those for angles in standard where. Two or more angles are angles in standard position where we follow the three steps listed above found... With something that looks a little like the right half of an angle finishes,. 'Ll show you how it works with two examples covering both positive and negative coterminal angles is! Down with the original angle was 52, adding 360 twice will give you 412 and.... Of 360, or 13/6 rad if you want to find coterminal angles in degrees, not,... Coterminal and smallest positive coterminal angles start at the starting angle 3/4 rad, the x-axis... /Eq } is outside the given interval, so it ca n't be our answer, or 2n there... Amazon associate, I earn from qualifying purchases that you may write 30 360! Around the other way, we find that 405 and -315 are the angle... Note: when the angle of 210210\degree210 ( 7/67\pi / 67/6 ): 570570\degree570 930930\degree930... Respective owners until the result is between 0 and 360 a positive coterminal angles= 200+ n * 360 degrees your... There are an infinite number of complete circles assume that 's in degrees is given in radians the... So, as well as the angle [ latex ] \theta =80^\circ [ /latex ] is with.