how to find the greatest negative coterminal angle

\u00a9 2023 wikiHow, Inc. All rights reserved. To 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 is measured in radians . Step 1: To find a positive angle, add 2: /6 + 2 = 13/6 Sketch the angle in standard position and draw an arrow representing the correct amount of rotation. 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. 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But you Step 2: Enter the angle in the given input box of the coterminal angles calculator. Therefore the ordered pair is \(\left(\dfrac{1}{2}, \dfrac{\sqrt{3}}{2}\right)\) and the secant value is \(\dfrac{1}{x}=\dfrac{1}{\dfrac{1}{2}}=2\). 4.1 Angle and Radian Measure 07:19 . By definition of coterminal angles, the negative angle that is equivalent to an angle of 285 is equal to - 75 degrees. 270 270 Since the angle 180 180 is in the third quadrant, subtract 180 180 from 270 270 . The angle \(90^{\circ}\) is coterminal with \(270^{\circ}\). 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. We can also use our knowledge of reference angles and ordered pairs to find the values of trig functions of angles with measure greater than 360 degrees. The distance from the origin to the point (1, 1) is (1 + 1) = 2. A negative angle moves in a clockwise direction. To find coterminal angles in steps follow the following process: If the given an angle in radians (3.5 radians) then you need to convert it into degrees: 1 radian = 57.29 degree so 3.5*57.28=200.48 degrees Now you need to add 360 degrees to find an angle that will be coterminal with the original angle: Trigonometry Examples Subtract 360 360 from 450 450 . The resulting angle of 40 40 is positive, less than 360 360 , and coterminal with 400 400 . Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. Recognizing that any angle has infinitely many coterminal angles explains the repetitive shape in the graphs of trigonometric functions. Example 1: Find a positive and a negative angle coterminal with a 55 angle. Find the angle between 0 and 360 (if in degrees) or between 0 rad and 2n rad (if in radians) that is coterminal with the given angle. Identify the least positive and greatest negative coterminal angles of each of the following angle measures. If told to find the least positive angle coterminal with 785 degrees you can use the following calculation process shown below. Coterminal Angle Calculator is a free online tool that displays the positive and negative coterminal angles for the given degree value. We can use this ordered pair to find the values of any of the trig functions of \(30^{\circ}\). Oblique Triangle Calculator (any other triangle), Circle Calculator (requires only one value). Answers may vary. To put it another way, 800 equals 80 plus two full rotations, as shown in Figure 18. Angles formed by two rays lie in the plane that contains the rays. 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. Required fields are marked *. One of the easiest methods for calculating coterminal angles is simply by adding or subtracting multiples of 360 from each angle measure until both values are within 180 of each other (or 0). asked by sara August 17, 2011 1 answer -417 + 360 = -57 doing another rotation would bring you into the positives answered by Reiny August 17, 2011 Answer this Question Still need help? There are 7 references cited in this article, which can be found at the bottom of the page. For instance, if you need to find a positive and negative coterminal of /4, adding 2 will give you the positive result 9/4 rad and subtracting will give you the negative -7/4 rad. This article was co-authored by wikiHow staff writer, Krysten Jackson. If two angles in standard position have the same terminal side, they are coterminal angles. Therefore the ordered pair is \(\left(\dfrac{\sqrt{2}}{2},\dfrac{\sqrt{2}}{2}\right)\) and the sine value is \(\dfrac{\sqrt{2}}{2}\). The vertex is fixed to the origin of the graph and the initial side, where the angle starts opening, runs along the x-axis. Example 1: Find a positive and a negative angle coterminal with a 55 angle. [1] If the . Trigonometry Examples Add 360 360 to 120 - 120 . Subtract [latex]2\pi [/latex] from the given angle. The angle [latex]\theta =80^\circ [/latex] is coterminal with 800. We measure angles starting from the positive x-axis, i.e. The formula to find the coterminal angles of an angle depending upon whether it is in terms of degrees or radians is: Degrees: 360 n Radians: 2n In the above formula, 360n, 360n means a multiple of 360, where n is an integer and it denotes the number of rotations around the coordinate plane. Here are 2 formulas: Given x as the angle you want to find coterminal angles to: The smallest nonnegative angle would be: (x-360floor (x/360)) And the largest nonpositive angle would be: (x-360ceil (x/360)) floor (x) is the floor function, that returns the greatest integer less than or equal to x, for instance: What happens to atoms during chemical reaction? Today, however, is different. Sketch the angle in standard position and draw an arrow representing the correct amount of rotation. These cookies track visitors across websites and collect information to provide customized ads. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. -315 is the negative coterminal angle of 45. Your Mobile number and Email id will not be published. It would be convenient to replace those out-of-range angles with a corresponding angle within the range of a single revolution. - 420 0; 5/4 radians 60 0; Find the angle between - 360 0 and 0 0 (if in degrees) or between 2 rad . Degrees = n360 Positive Coterminal Angles 50 + 360 = 410 50 + (2 360) = 770 50 + (3 360) = 1130 The greatest negative coterminal . This gives you the least negative coterminal angle. Accessibility StatementFor more information contact us atinfo@libretexts.org. Solve for more than one coterminal angle by adding or subtracting a full revolution multiple times. Also both have their terminal sides in the same location. Find the Reference Angle -450 450 - 450 Find an angle that is positive, less than 360 360 , and coterminal with 450 - 450 . Solution for Find the least positive and the greatest negative coterminal angles of the following angle measures. For the starting angle 3/4 rad, the most negative coterminal angle would be -5/4 rad. But opting out of some of these cookies may affect your browsing experience. Find the least positive angle [latex]\theta [/latex] that is coterminal with an angle measuring 800, where [latex]0^\circ \le \theta <360^\circ [/latex]. To determine the coterminal angle between 0\degree 0 and 360\degree 360, all you need to do is to calculate the modulo - in other words, divide your given angle by the 360\degree 360 and check what the remainder is. b. Below is a 30 angle in standard position. That angle also shares the same initial and terminal sides. Then, we can decide if we want to add or subtract multiples of 360 or of 2 depending on whether we want to obtain a positive or negative . Coterminal Angles - Positive and Negative, Converting Degrees to Radians, Unit Circle, Trigonometry 10:20 14.19 MB 813,095. If your original angle was 52, adding 360 twice will give you 412 and 772. Ask a New Question what is the largest negative coterminal angle of -417? From your studies at school, you know that this is the equivalent of a "negative angle". Finding angles coterminal with radian values can be done the same way. 55 360 = 305 55 + 360 = 415 This angle opens in a counterclockwise direction. This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. Coterminal angles are two angles in standard position that have the same terminal side. 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. But both angles have the same terminal side. For example, notice that 45 degrees and -315 degrees are coterminal angles because they both start and stop at the same place, but just differ in their amount or direction of rotation. Get 5 free video unlocks on our app with code GOMOBILE, Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger, Find a positive angle and a negative angle that are coterminal with the given angle. The cookie is used to store the user consent for the cookies in the category "Analytics". In general, if a negative angle has a reference angle of \(30^{\circ}\), \(45^{\circ}\), or \(60^{\circ}\), or if it is a quadrantal angle, we can find its ordered pair, and so we can determine the values of any of the trig functions of the angle. She has contributed her editing skills to multiple content teams and publishing houses. Type an integer or a fraction.) Coterminal angles are angles that stop opening at the same place when drawn in the standard position. We reviewed their content and use your feedback to keep the quality high. If told to find the least positive angle coterminal with 785 degrees you can use the following calculation process shown below. and more. Solved by verified expert. - 25 0; 110 0; 11/6 radians-5/4 radiansFind the angle between 0 0 and 360 0 (if in degrees) or between 0 rad and 2 rad (if in radians) that is coterminal with the given angle. Then find the measure of the negative angle that is coterminal with A and. - 250 2. $$ \frac{7 \pi}{6} - 2\pi = \frac{7 \pi}{6} - \frac{12 \pi}{6} = -\frac{5 \pi}{6} $$ So, a negative coterminal angle is $-\frac{5 \pi}{6}$. - 250 2. Two or more angles are said to be co-terminal when they have the same initial and terminal sides. For other applications, we may need another type of conversion. The angle \(270^{\circ}\) is coterminal with \(90^{\circ}\). Therefore the ordered pair of points is \((-1, 0)\). Negative Vs Positive Angle. Step 3: Click on the "Calculate" button to find the coterminal angles. In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. In Mathematics, the coterminal angle is defined as an angle, where two angles are drawn in the standard position. We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. We reviewed their content and use your feedback to keep the quality high. Find the value of the following expressions: \(\sin(45^{\circ} )=\dfrac{\sqrt{2}}{2}\). The two rays are called the sides of the angle while the common endpoint is called the vertex of the angle. 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. The angle 90^{\circ}\) is coterminal with \(270^{\circ}\). This image may not be used by other entities without the express written consent of wikiHow, Inc.
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