how to find the greatest negative coterminal angle

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. - 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. These angles are obtained by adding or subtracting 360 from the given angle. This works great if you need to find both a positive and a negative coterminal angle. The resulting coterminal for this equation is -11/6 rad, or -330 if you need to. To find the coterminal angle, just add or subtract 360 or 2 from the angle. 11) 185 , 545 12) 17 36, 161 36 Find a coterminal angle between 0 and 360. The problem specifically asked for a negative angle, so the process needs to take place one more time. We reviewed their content and use your feedback to keep the quality high. Coterminal angles are two angles in standard position that have the same terminal side. Thanks to all authors for creating a page that has been read 5,859 times. - 250 2. [1] Look at Figure 16. 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. 90 90 . Find the value of the following expressions: \(\sin(45^{\circ} )=\dfrac{\sqrt{2}}{2}\). Take note that n is an integer. Determine if the flowing pairs of angles are coterminal. Activity 7: A. To find the least negative angle coterminal with another angle, say 78 pi, the calculation process is shown below will work. the initial side of an angle measure is usually the positive x-axis. 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. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. We can find coterminal angles measured in radians in much the same way as we have found them using degrees. Recall that graphing a negative angle means rotating clockwise. Home Geometry Angle Coterminal Angles. Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors. This cookie is set by GDPR Cookie Consent plugin. Earlier, you were asked if it is still possible to find the values of trig functions for the new type of angles. 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: Recognizing that any angle has infinitely many coterminal angles explains the repetitive shape in the graphs of trigonometric functions. Find an angle [latex]\alpha [/latex] that is coterminal with an angle measuring 870, where [latex]0^\circ \le \alpha <360^\circ [/latex]. Subtract 360 360 from 400 400 . These cookies ensure basic functionalities and security features of the website, anonymously. But both angles have the same terminal side. Name a point on the terminal side of the angle. The angle \(300^{\circ}\) is in the \(1^{st}\) quadrant and has a reference angle of \(60^{\circ}\). 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. [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. Subtracting one revolution would be considered the smallest negative coterminal angle. The resulting angle of 90 90 is positive, less than 360 360 , and coterminal with 450 450 . Video: Evaluating Trigonometric Functions of Any Angle - Overview, Practice: Trigonometric Functions of Negative Angles. Analytical cookies are used to understand how visitors interact with the website. Once this number is found, it must again get subtracted from the given angle 526 degrees. 11?/6 radians 4. References. It also shows you how to convert radians to degrees and degrees to radians. This image may not be used by other entities without the express written consent of wikiHow, Inc.
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