Find all solution 7cos (3x)−1= 3 for x over the interval [ 0,2π ]


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Question Number 126005 by bramlexs22 last updated on 16/Dec/20

$F i n d a l l s o l u t i o n 7 \cos (3 x) - 1 = 3$ $f o r x o v e r t h e i n t e r v a l [0, 2 π]$
Commented by liberty last updated on 16/Dec/20
$7 cos (3x)=4 ⇒cos (3x)=(4/7) 3x = cos^(−1) ((4/7)) = 0.963 3x = { ((0.963+k.2π)),((−0.963+k.2π)) :} ⇔ x= { ((0.321+((2kπ)/3))),((−0.321+((2kπ)/3))) :}$
$7 \cos (3 x) = 4 \Rightarrow \cos (3 x) = \frac{4}{7}$ $3 x = \cos^{- 1} (\frac{4}{7}) = 0.963$ $3 x = {\begin{cases} 0.963 + k . 2 π \\ - 0.963 + k . 2 π \end{cases} \Leftrightarrow x = {\begin{cases} 0.321 + \frac{2 k π}{3} \\ - 0.321 + \frac{2 k π}{3} \end{cases}$
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