This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. To find a positive coterminal angle, we can add $2\pi$ to the given angle: $\pi + 2\pi = 3\pi$. 360n. That angle also shares the same initial and terminal sides. The sine is the "\(y\)" coordinte, so here it is -1. Find an angle [latex]\beta [/latex] that is coterminal with an angle measuring 300 such that [latex]0^\circ \le \beta <360^\circ [/latex]. Recognizing that any angle has infinitely many coterminal angles explains the repetitive shape in the graphs of trigonometric functions. Trigonometry. For example, 100 and 460 are coterminal for this reason, as is 260. c. Name another angle that is coterminal with the angle you have drawn. Find the value of the expression: \(\sin90^{\circ}\). 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]. 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. How to find greatest negative coterminal angle - Math Theorems 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 . algebra / trigonometry / Activity 7: A. Oh no! A negative angle moves in a clockwise direction. For example, if one angle measures 450 and another angle measures 210 then you would subtract 360 from 450 (450-360 = 90) making both . What is the measure of angle T?, What are the two possible measures of the angle below? Subtract 360 360 from 400 400 . The angle \(270^{\circ}\) is coterminal with \(90^{\circ}\). This gives you the least negative coterminal angle. Figure 16. It would be convenient to replace those out-of-range angles with a corresponding angle within the range of a single revolution. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. Coterminal Angles 55 360 = 305 55 + 360 = 415 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. Draw each of the following angles in standard position and then do the 270 270 Since the angle 180 180 is in the third quadrant, subtract 180 180 from 270 270 . Sketch the angle in standard position and draw an arrow representing the correct amount of rotation. 2.3.8: Trigonometric Functions of Negative Angles Finding coterminal angles may sound tricky at first, but the formula is actually very simple once you get the hang of it. For example, the negative coterminal angle of 100 is 100 - 360 = Solve math equation 11) 185 , 545 12) 17 36, 161 36 Find a coterminal angle between 0 and 360. Coterminal angles are angles that have the same terminal side. [1] Coterminal angles are angles that stop opening at the same place when drawn in the standard position. 4.1 Angle and Radian Measure 07:19 . Find an angle between -500 and +500 and that is coterminal with = 75. Accessibility StatementFor more information contact us atinfo@libretexts.org. $$-\frac{2 \pi}{3}$$, Find a positive angle and a negative angle that are coterminal with the given angle. This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. 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. Here 405 is the positive coterminal angle, -315 is the negative coterminal angle. =660 =660 +360 =1020 =1020 +360 =1380 NOTE: =1380 =1020 +360 =(660 +360 )+360 =660 +2(360 ) Krysten graduated from Northwestern University in 2019 with a B.A. By definition of coterminal angles, the negative angle that is equivalent to an angle of 285 is equal to - 75 degrees. Negative Vs Positive Angle. An angles reference angle is the measure of the smallest, positive, acute angle [latex]t[/latex] formed by the terminal side of the angle [latex]t[/latex] and the horizontal axis. Negative angles and angles greater than a full revolution are more awkward to work with than those in the range of 0 to 360, or 0 to [latex]2\pi [/latex]. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/6\/61\/Find-Coterminal-Angles-Step-1.jpg\/v4-460px-Find-Coterminal-Angles-Step-1.jpg","bigUrl":"\/images\/thumb\/6\/61\/Find-Coterminal-Angles-Step-1.jpg\/v4-728px-Find-Coterminal-Angles-Step-1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"