December 19th, 2018, 08:38 AM  #1 
Newbie Joined: Dec 2018 From: Usa Posts: 2 Thanks: 0  Solving in R
Hello, I recently came here invited by a friend of mine into the forum, bless who can give me as much as details about this ^^ 1) Solve in R cos(3x)=1/2 2) Calculate cos(3x) according to cos(x) Last edited by skipjack; December 19th, 2018 at 12:04 PM. 
December 19th, 2018, 08:47 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,887 Thanks: 1506  
December 19th, 2018, 08:55 AM  #3 
Newbie Joined: Dec 2018 From: Usa Posts: 2 Thanks: 0  
December 19th, 2018, 09:16 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,887 Thanks: 1506  
December 19th, 2018, 11:50 AM  #5  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,640 Thanks: 2624 Math Focus: Mainly analysis and algebra  Quote:
For 2) you will need to use the identities \begin{align}\cos{(A+B)} &= \cos{(A)}\cos{(B)}  \sin{(A)}\sin{(B)} \\ \sin{(A+B)} &= \sin{(A)}\cos{(B)} + \cos{(A)}\sin{(B)} &\text{and} \\ \cos^2{(A)} + \sin^2{(A)} &= 1\end{align} to turn $(3x)$ into $(2x + x)$, $(2x)$ into $(x + x)$ and finally eliminate $\sin^2{(x)}$ from the result.  

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