if-sin-x-x-20-20-find-x-

Question Number 61162 by Tawa1 last updated on 29/May/19

if \sin (x) = \frac{x - 20}{20}, find x

Commented by kaivan.ahmadi last updated on 29/May/19

w e c a n f i n d n u m b e r o f s o l u t i o n b y p l o t e

y = s i n x a n d y = \frac{x - 20}{20}

t h i s e q u a t i o n h a s 13 a n s w e r

Commented by maxmathsup by imad last updated on 29/May/19

(e) \Leftrightarrow s i n (x) = \frac{x}{20} - 1 c h a n g e m e n t \frac{x}{20} = t g i v e

s i n (20 t) = t - 1 \Leftrightarrow s i n (20 t) - t + 1 = 0

l e t f (t) = s i n (20 t) - t + 1 \Rightarrow f^{^{'}} (t) = 20 c o s (t) - 1

f^{^{'}} (t) = 0 \Rightarrow 20 c o s t = 1 \Leftrightarrow c o s t = \frac{1}{20} l e t α / c o s (α) = \frac{1}{20} \Rightarrow

t = α + 2 k π o r t = - α + 2 k π \Rightarrow t = a r c o s (\frac{1}{20}) + 2 k π o r

t = - a r c o s (\frac{1}{20}) + 2 k π i n t h i s c a s e i t b e t t e r t o u s e n e w t o n

m e t h o d t o a p p r o x i m a t e t h e r o o t s \dots .

Commented by Tawa1 last updated on 30/May/19

God bless you sir

Answered by malwaan last updated on 29/May/19

- 1 ⩽ s i n (x) ⩽ 1

\Rightarrow - 1 ⩽ \frac{x - 20}{20} ⩽ 1

\Rightarrow - 20 ⩽ x - 20 ⩽ 20

\Rightarrow 0 ⩽ x ⩽ 40

\Rightarrow x \in [0; 40]

Commented by Tawa1 last updated on 30/May/19

God bless you sir

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