http://www.mapleprimes.com/posts/40167-Trig-Equation en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Thu, 11 Jun 2026 22:11:51 GMT Thu, 11 Jun 2026 22:11:51 GMT The latest comments added to the Post, trig equation http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/posts/40167-Trig-Equation http://www.mapleprimes.com/posts/40167-Trig-Equation?ref=Feed:MaplePrimes:trig equation:Comments#comment73888 After plotting, you can enter your range into the Roots command found in the Student[Calculus1] package. >restart: >with(Student[Calculus1]): >Roots(cos(x/2)-1/2,x=0..12); <maple>[2/3*Pi, 10/3*Pi]</maple> <em>Regards, Georgios Kokovidis Dräger Medical</em> The latest comments added to the Post, trig equation 73888 Mon, 28 Jan 2008 05:32:00 Z gkokovidis gkokovidis http://www.mapleprimes.com/posts/40167-Trig-Equation?ref=Feed:MaplePrimes:trig equation:Comments#comment73886 Roots does not indicate, as solve does, that there is an infinity of solutions accessed by adding 4k Pi. Is there a Maple command that will give both pieces of information? Alla The latest comments added to the Post, trig equation 73886 Mon, 28 Jan 2008 07:35:23 Z alla alla http://www.mapleprimes.com/posts/40167-Trig-Equation?ref=Feed:MaplePrimes:trig equation:Comments#comment73885 Note that the binary variable _B1 takes the values 0 and 1, while _Z1 takes arbitrary integer values. For _B1 = 0: <pre> > S := 2/3*Pi-4/3*Pi*_B1+4*Pi*_Z1: seq(eval(S,{_B1=0,_Z1=z}),z=-3..3); </pre> <maple>-34/3*Pi</maple>,<maple> -22/3*Pi</maple>,<maple> -10/3*Pi</maple>,<maple> 2/3*Pi</maple>,<maple> 14/3*Pi</maple>,<maple> 26/3*Pi</maple>,<maple> 38/3*Pi</maple> For _B1 = 1: <pre> > seq(eval(S,{_B1=1,_Z1=z}),z=-3..3); </pre> <maple>-38/3*Pi</maple>,<maple> -26/3*Pi</maple>,<maple> -14/3*Pi</maple>,<maple> -2/3*Pi</maple>,<maple> 10/3*Pi</maple>,<maple> 22/3*Pi</maple>,<maple> 34/3*Pi</maple> So the smallest positive values are 2/3*Pi and 10/3*Pi. The latest comments added to the Post, trig equation 73885 Mon, 28 Jan 2008 07:39:58 Z Robert Israel Robert Israel http://www.mapleprimes.com/posts/40167-Trig-Equation?ref=Feed:MaplePrimes:trig equation:Comments#comment73884 Pertaining to the original example, solve by itself does not return {x = 2/3*Pi-4/3*Pi*_B2+4*Pi*_Z4} unless the environment variable _EnvAllSolutions is set to true. I mention this just in case others try to recreate the result and only see one solution returned. >_EnvAllSolutions := true: <em>Regards, Georgios Kokovidis Dräger Medical</em> The latest comments added to the Post, trig equation 73884 Mon, 28 Jan 2008 07:47:43 Z gkokovidis gkokovidis http://www.mapleprimes.com/posts/40167-Trig-Equation?ref=Feed:MaplePrimes:trig equation:Comments#comment73877 Once again it has proven rewarding to read these threads: <ul> <li>I did not know that <code>_B1</code>, <code>_B2</code>, etc., meant binary variables taking on values <code>0</code> and <code>1</code> only, as <a href="http://www.mapleprimes.com/blog/alla/trig-equation#comment-12732">Robert writes</a>. </li> <li>I did not know that <code>_EnvAllSolutions</code> must be assigned <code>true</code> in order that <code>solve</code> returns all solutions to some trigonometric equation, as <a href="http://www.mapleprimes.com/blog/alla/trig-equation#comment-12733">Georgios writes</a>. </li> </ul> Thanks, guys! The latest comments added to the Post, trig equation 73877 Mon, 28 Jan 2008 13:17:09 Z John Fredsted John Fredsted http://www.mapleprimes.com/posts/40167-Trig-Equation?ref=Feed:MaplePrimes:trig equation:Comments#comment84339 Instead of using _EnvAllSolutions, I prefer to pass the AllSolutions option to solve: <code>solve(cos(x/2) = 1/2, x, AllSolutions);</code> it does the same thing, but it is more localized. -- John May The latest comments added to the Post, trig equation 84339 Mon, 28 Jan 2008 20:12:54 Z jpmay jpmay