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 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
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Quote:
 Originally Posted by AnasMathZ 1) Solve in R cos(3x)=1/2 2) Calculate cos(3x) according to cos(x)
note ...

$\cos(u) = \dfrac{1}{2}$ at $u = 2k\pi \pm \dfrac{\pi}{3} \, ; \, k \in \mathbb{Z}$

December 19th, 2018, 08:55 AM   #3
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Quote:
 Originally Posted by skeeter note ... $\cos(u) = \dfrac{1}{2}$ at $u = 2k\pi \pm \dfrac{\pi}{3} \, ; \, k \in \mathbb{Z}$
you think you can solve it for me ?

December 19th, 2018, 09:16 AM   #4
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Quote:
 Originally Posted by AnasMathZ you think you can solve it for me ?
you try and solve it ... start by letting $u=3x$

December 19th, 2018, 11:50 AM   #5
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Quote:
 Originally Posted by AnasMathZ 1) Solve in R cos(3x)=1/2 2) Calculate cos(3x) according to cos(x)
skeeter has given you enough to solve 1). If you write $u=3x$ you get $\cos{(3x)} = \frac12$. You should know what values of $u$ give that result (and skeeter has told you that too). Then $3x=u$ gives you a simple equation to determine $x$.

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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