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Question Number 61162 by Tawa1 last updated on 29/May/19
if sin(x) = ((x − 20)/(20)) , find x
ifsin(x)=x−2020,findx
Commented by kaivan.ahmadi last updated on 29/May/19
we can find number of solution by plote y=sinx and y=((x−20)/(20)) this equation has 13 answer
wecanfindnumberofsolutionbyplotey=sinxandy=x−2020thisequationhas13answer
Commented by maxmathsup by imad last updated on 29/May/19
(e) ⇔sin(x) =(x/(20)) −1 changement (x/(20)) =t give sin(20t) =t−1 ⇔ sin(20t)−t +1 =0 let f(t) =sin(20t)−t+1 ⇒f^′ (t) =20cos(t)−1 f^′ (t) =0 ⇒20cost =1 ⇔cost =(1/(20)) let α /cos(α)=(1/(20)) ⇒ t =α +2kπ or t =−α +2kπ ⇒t =arcos((1/(20)))+2kπ or t =−arcos((1/(20))) +2kπ in this case it better to use newton method to approximate the roots....
(e)⇔sin(x)=x20−1changementx20=tgivesin(20t)=t−1⇔sin(20t)−t+1=0letf(t)=sin(20t)−t+1⇒f′(t)=20cos(t)−1f′(t)=0⇒20cost=1⇔cost=120letα/cos(α)=120⇒t=α+2kπort=−α+2kπ⇒t=arcos(120)+2kπort=−arcos(120)+2kπinthiscaseitbettertousenewtonmethodtoapproximatetheroots….
Commented by Tawa1 last updated on 30/May/19
God bless you sir
Godblessyousir
Answered by malwaan last updated on 29/May/19
−1≤sin(x)≤1 ⇒−1≤((x−20)/(20))≤1 ⇒−20≤x−20≤20 ⇒0≤ x≤40 ⇒x∈[ 0 ; 40]
−1⩽sin(x)⩽1⇒−1⩽x−2020⩽1⇒−20⩽x−20⩽20⇒0⩽x⩽40⇒x∈[0;40]
Commented by Tawa1 last updated on 30/May/19
God bless you sir
Godblessyousir

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