The-number-of-intersecting-points-on-the-graph-for-sin-x-x-10-for-x-pi-pi-is-

Question Number 16675 by Tinkutara last updated on 25/Jun/17

The number of intersecting points on

the graph for \sin x = \frac{x}{10} for x \in [- π, π]

is

Answered by ajfour last updated on 25/Jun/17

Commented by Tinkutara last updated on 25/Jun/17

I know the answer is 3 but can we find

the algebraic values for this equation ?

Commented by ajfour last updated on 25/Jun/17

y = \frac{x}{10} barely rises till y = \frac{π}{10}

when x = π . So 3 intersection

points for x \in [- π, π] .

Commented by ajfour last updated on 25/Jun/17

I cannot find the values, but

how about total number of

intersection points ?

Commented by Tinkutara last updated on 25/Jun/17

I {don}^{'} t have an idea to solve total

number of intersection points .

Commented by mrW1 last updated on 25/Jun/17

see Q 16699 for total number of inter -

section points

Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 25/Jun/17

s i n x ≅ x - \frac{x^{3}}{6} \Rightarrow x - \frac{x^{3}}{6} = \frac{x}{10} \Rightarrow

60 x - 10 x^{3} = 6 x \Rightarrow x (54 - 10 x^{2}) = 0

\Rightarrow x = 0, x = \pm \sqrt{\frac{54}{10}} = \pm 2.32

\Rightarrow x = 0, \pm 2.32 (e q u a t i o n h a v e 3 a n s w e r s) .

t h e r e i s a l i t t l e d i f f e r e n c e b e t w e e n

t h e s e a n s w e r s a n d g r a p h i c m e t h o d .

i t i s n o t s o g o o d, b u t y o u c a n u s e t h i s

w a y f o r f i n d i n g n u m b e r o f a n s w e r s .

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

m o r e t e r m s i n e x p r i s s i o n o f^{'} {s i n x}^{'} .