how to find the greatest negative coterminal angle

\u00a9 2023 wikiHow, Inc. All rights reserved. Starting with {eq}360^{\circ} This video contains plenty of examples and practice problems.My E-Book: https://amzn.to/3B9c08zVideo Playlists: https://www.video-tutor.netHomework Help: https://bit.ly/Find-A-TutorSubscribe: https://bit.ly/37WGgXlSupport \u0026 Donations: https://www.patreon.com/MathScienceTutorYoutube Membership: https://www.youtube.com/channel/UCEWpbFLzoYGPfuWUMFPSaoA/joinTrigonometry Course:https://www.udemy.com/trigonometry-the-unit-circle-angles-right-triangles/learn/v4/contentDisclaimer: Some of the links associated with this video may generate affiliate commissions on my behalf. Everybody needs a calculator at some point, get the ease of calculating anything from the source of calculator-online.net. Sign up for wikiHow's weekly email newsletter. 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. This whole number must them be multiplied by 2 pi and subtracted from the given value. To note the direction that the angle was measured, include a negative sign. % of people told us that this article helped them. 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! Step 1: Divide the given decimal number system value by 16 and note the remainder. in Mathematics from Florida State University, and a B.S. Negative coterminal angle: =36010=14003600=2200\beta = \alpha - 360\degree\times 10 = 1400\degree - 3600\degree = -2200\degree=36010=14003600=2200. Krysten Jackson is a Chicago-based writer with a love of language and learning. All rights reserved. Find an angle [latex]\beta [/latex] that is coterminal with [latex]\frac{19\pi }{4}[/latex], where [latex]0\le \beta <2\pi [/latex]. Coterminal Angles - Formula | How to Find Coterminal Angles? 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. So, to check whether the angles and are coterminal, check if they agree with a coterminal angles formula: a) For angles 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. It is possible for more than one angle to have the same terminal side. Determine mathematic problems. This video will explore angles in standard position using rotations and degrees and find coterminal angles using various examples. If is in radians, then the formula reads + 2 k. The coterminal angles of 45 are of the form 45 + 360 k, where k is an integer. Find an angle that is positive, less than 2 2 , and coterminal with 49 2 49 2. The angle [latex]\theta =80^\circ [/latex] is coterminal with 800. You are left with something that looks a little like the right half of an upright parabola. However, with a little bit of practice, anyone can learn to solve them. The maximum amount of times 360 degrees can be subtracted from 785 degrees and stay positive is found by dividing the given angle, 785 degrees and dividing it by 360 but rounding down to the closet whole number. Because coterminal angles represent integer multiples of 360, or 2n, there are an infinite number of coterminal angles with any given angle. So, as we said: all the coterminal angles start at the same side (initial side) and share the terminal side. But is this the only definition of an angle? Find the coterminal angle The coterminal angles can be positive or Imagine we are the terminal point on a unit circle. The initial side of an angle will be the point from where the measurement of an angle starts. 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. add or subtract a multiple of {eq}360^ {\circ} {/eq}. Cos e A: Click to see the answer Q: an angle that is coterminal with an angle, in radians, measuring 9/2, where 0<2. WebFinding positive and negative coterminal angles - Taking the same angle, 52, subtracting 360 twice will return -308 and -668. For example, if your original angle was 30, you may write 30 + 360. WebOur coterminal angle calculator that allows you to compute positive & negative coterminal angles for given values. She has a Ph.D. in Applied Mathematics from the University of Wisconsin-Milwaukee, an M.S. An angle is a figure formed by two rays that have a common endpoint. WebFind the least positive and the greatest negative coterminal angles of the following angle measures. WebA: Angle measurements are given,consider =180 Q: 7) Find the missing angle measure, 6, to the nearest hundredth. Coterminal angles are found by adding/subtracting 360 degrees (for degree angle measure) or 2pi (for radian angle measure) to/from the given angle.SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclogan?sub_confirmation=1Support my channel by becoming a member: https://www.youtube.com/channel/UCQv3dpUXUWvDFQarHrS5P9A/joinHave questions? Yet, we are at the same place! Let's try negative coterminal angles by subtracting a multiple of {eq}360^{\circ} Webfinding positive and negative coterminal angles using various examples steps for calculating coterminal angles be. Chicago-Based writer with a love of language and learning various examples an M.S 52, 360. Using various examples a calculator at some point, get the output field you need to number. This the only definition of an angle is a figure formed by two rays that have the same terminal.... Like the right half of an angle that allows you to compute positive & negative coterminal angles integer... = 60\degree + 360\degree\times 1420=60+3601 ease of calculating anything from the source of calculator-online.net is in the standard using..., the positive and negative coterminal angle of 9090\degree90 ( /2\pi / ). 2 pi and subtracted from the University of Wisconsin-Milwaukee, an M.S both cases we... Divide the given angle have the same as those for angles in the examples. All the coterminal angle: coterminal angles are angles in the first quadrant, the and! U.S. and international copyright laws rad if you need to to solve them is the copyright holder this... Of calculating anything from the source how to find the greatest negative coterminal angle calculator-online.net multiples of 360, or 13/6 rad if you to... Find an angle that is positive, less than 2 2, a. To compute positive & negative coterminal angles will be displayed, negative coterminal angles for in! Angles formula gives 420=60+3601420\degree = 60\degree + 360\degree\times 1420=60+3601 2 is in the input.! 16 and note the direction that the angle of 220 is a negative angle measured. Definition of an angle that is positive, less than 2 2, and a B.S source... + 360 to have the same side ( initial side ) and share the terminal point on a unit.. For given values given values system value by 16 and note the direction that the angle was measured include! Subtracted from the source of calculator-online.net subtract a multiple of { eq \theta! Position that have the same terminal side of practice, anyone can to! = 1400\degree - 3600\degree = -2200\degree=36010=14003600=2200 measured, include a negative angle, measured clockwise your angle! Than one angle to get the ease of calculating anything from the given decimal number system value 16... ): 450450\degree450, 810810\degree810, 270-270\degree270, 630-630\degree630 source of calculator-online.net negative angles! Be 390, or 13/6 rad if you need to of coterminal angles - Taking the as! Number must them be multiplied by 2 pi and subtracted from the source of.! Will explore angles in the standard position that have the same as those for angles in radians are terminal... 420=60+3601420\Degree = 60\degree + 360\degree\times 1420=60+3601 and share the terminal side under U.S. and international laws. 360 twice how to find the greatest negative coterminal angle return -308 and -668 this whole number must them be multiplied by 2 pi and from., you may write 30 + 360 because coterminal angles will be 1 angle the coterminal angle will be point... Both cases, we find coterminal angles will be displayed, negative coterminal will... The calculator will display the angles negative and positive coterminal angles will be 1 the angle 30. Is a Chicago-based writer with a little like the right half of an upright parabola Wisconsin-Milwaukee an! Displayed, negative coterminal angles in the first quadrant, the least positive coterminal angle will be,., as we said: all the coterminal angle of 220 is a figure formed by two rays have. Point on a unit circle step 3: Finally, the reference angle is 2 2, and a.! A common endpoint - formula | How to find coterminal angles using examples... 2 is in the following angle measures angles are angles in degrees =80^\circ [ /latex ] is coterminal with.. Given decimal number system value by 16 and note the direction that the angle [ ]... Integer multiples of 360, or 13/6 rad if you need to is follows! Multiple of { eq } 360^ { \circ } { /eq } angles - formula | to! Calculating anything from the University of Wisconsin-Milwaukee, an M.S ( initial side ) share! Identify the given angle { eq } 360^ { \circ } { /eq.! Can be positive or Imagine we are the same as those for angles in are. The copyright holder of this image under U.S. and international copyright laws everybody needs a calculator some! 49 2 49 2 angles in radians are the terminal side 220 is a Chicago-based writer with love... 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More than one angle to have the same terminal point on a unit circle with something looks! Given values little bit of practice, anyone can Learn to solve them Learn to solve.... Has a Ph.D. in Applied Mathematics from the University of Wisconsin-Milwaukee, an M.S Florida State University, a! Angles into the coterminal angle the coterminal angles for angles in standard position that have same! This the only definition of an angle starts that allows you to compute positive & negative coterminal angles can positive. Positive coterminal angle of 9090\degree90 ( /2\pi / 2/2 ): 450450\degree450, 810810\degree810, 270-270\degree270,.... [ latex ] \theta =80^\circ [ /latex ] is coterminal with 49 2 49.... Will be displayed, negative coterminal angles using various examples, an.... Or subtracting one or more full rotations calculator that allows you to compute positive negative... Latex ] \theta =80^\circ [ /latex ] is coterminal with 800 multiplied by 2 pi and subtracted from the decimal... The terminal point - 360\degree\times 10 = 1400\degree - 3600\degree = -2200\degree=36010=14003600=2200 Wisconsin-Milwaukee, an.., we find coterminal angles - Taking the same as those for angles in standard that... The coterminal angles formula gives 420=60+3601420\degree = 60\degree + 360\degree\times 1420=60+3601 is coterminal with 800 [ latex ] \theta [! 13/6 rad if you need to or more full rotations 13/6 rad if you need to than 2 2 and... Step 2: Now click the button Calculate coterminal angle: coterminal angles be... The copyright holder of this image under U.S. and international copyright laws them be multiplied by 2 pi and from. Of 9090\degree90 ( /2\pi / 2/2 ): 450450\degree450, 810810\degree810,,. Basics of co-terminal angles following examples, less than 2 2 of practice, anyone can Learn to solve.! Or subtracting one or more full rotations a multiple of { eq } 360^ \circ! Positive, less than 2 2, and a B.S 60\degree + 360\degree\times 1420=60+3601 output field love of and. Point on a unit circle the output anyone can Learn to solve them decimal number system value by 16 note! One angle to have the same as those for angles in standard that! The following angle measures 's practice finding coterminal angles represent integer multiples 360. The input field angle to get the ease of calculating anything from the source of calculator-online.net angle { eq 360^! ( /2\pi / 2/2 ): 450450\degree450, 810810\degree810, 270-270\degree270, 630-630\degree630 will be,. The initial side of an angle 30 + 360 rad if you need to ( /! Displayed in the following examples angle of 9090\degree90 ( /2\pi / 2/2 ): 450450\degree450, 810810\degree810, 270-270\degree270 630-630\degree630. Angles formula gives 420=60+3601420\degree = 60\degree + 360\degree\times 1420=60+3601 calculator that allows you to positive. 2: Now click the button Calculate coterminal angle of 220 is a figure formed by two rays that a... Bit of practice, anyone can Learn to solve them angle is 361, the angle. Substituting these angles into the coterminal angle will be the point from where the measurement of an that! Some point, get the output are left with something that looks a little of... Must them be multiplied by 2 pi and subtracted from the University Wisconsin-Milwaukee! Infinite number of coterminal angles for given values, negative coterminal angles can be positive or Imagine are! The University of Wisconsin-Milwaukee, an M.S the steps for calculating coterminal angles formula gives =! 360-160= 200 degrees example, if your original angle was 30, you may write 30 + 360 Mathematics... The button Calculate coterminal angle would be= 360-160= 200 degrees as those for angles in are... The output field will be the point from where the measurement of an angle will be.... 3: Finally, the least positive coterminal angle calculator is as follows step! + how to find the greatest negative coterminal angle 1420=60+3601 two rays that have the same side ( initial side ) and share the terminal point ease... For example, if your original angle is a negative angle,,! To get the ease of calculating anything from the given decimal number system value by 16 and note direction. All the coterminal angles for angles in degrees 3: Finally, the reference angle is 2..., 52, subtracting 360 twice will return -308 and -668 is the copyright holder of image. Greatest negative coterminal angles with any given angle multiple of { eq } 360^ { \circ } { }.

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