My Math Forum indicate least positive angle

 Trigonometry Trigonometry Math Forum

 August 27th, 2016, 04:22 PM #1 Newbie   Joined: Aug 2016 From: Brazil Posts: 8 Thanks: 0 indicate least positive angle Indicate the smallest positive angle that verifies the equation $\displaystyle \cos(\frac{x}{4}) + \cos(\frac{x}{5}) + 3\cos(\frac{x}{10}) + 3\cos\frac{x}{20}=0$ ANSWER $\displaystyle \frac{20\pi}{3}$ Thank You Last edited by skipjack; August 28th, 2016 at 01:56 AM.
 August 28th, 2016, 12:33 AM #2 Newbie   Joined: Dec 2006 Posts: 5 Thanks: 2 Transform the sums in products using the formula $\displaystyle \cos a+\cos b=2\cos\frac{a+b}{2}\cos\frac{a-b}{2}$ and we have $\displaystyle 2\cos\frac{9x}{40}\cos\frac{x}{40}+6\cos\frac{3x}{ 40}\cos\frac{x}{40}=0$ $\displaystyle 2\cos\frac{x}{40}\left(\cos\frac{9x}{40}+ 3\cos\frac{3x}{40}\right)=0$ Then $\displaystyle \cos\frac{x}{40}=0\Rightarrow x=20\pi$ or $\displaystyle \cos\frac{9x}{40}+3\cos\frac{3x}{40}=0$ Now we use the formula $\displaystyle \cos 3a=4\cos^3a-3\cos a$ and the equation becomes $\displaystyle 4\cos^3\frac{3x}{40}=0\Rightarrow \frac{3x}{40}=\frac{\pi}{2}\Rightarrow x=\frac{20\pi}{3}$ Thanks from Nathalia Last edited by skipjack; August 28th, 2016 at 01:58 AM.

 Tags angle, positive

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post GIjoefan1976 Algebra 4 February 16th, 2016 12:55 PM randomgamernerd Geometry 2 November 17th, 2015 08:03 AM Tangeton Trigonometry 4 January 9th, 2015 03:13 AM Gyiove Algebra 1 February 26th, 2014 04:57 PM kingkos Algebra 2 December 7th, 2012 05:34 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top