the total no of solution of sin{x}=cos{x} where{x} denotes fractional part of x in [o 2π]is equal to ans:6


Question and Answers Forum

All Questions Topic List
Trigonometry Questions
Previous in All Question Next in All Question
Previous in Trigonometry Next in Trigonometry
Question Number 48851 by vajpaithegrate@gmail.com last updated on 29/Nov/18
$the total no of solution of sin{x}=cos{x} where{x} denotes fractional part of x in [o 2π]is equal to ans:6$
$the total no of solution of \sin {x} = \cos {x}$ $where {x} denotes fractional part of x in$ $[o 2 π] is equal to$ $ans : 6$
Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18
$sin{x}=cos{x} sin(x−[x])=cos(x−[x]) x={x}+[x] {x}=fractional part function [x]=greatest integer function from graph it is seen that in [0,2π] six(06) solution$
$s i n {x} = c o s {x}$ $s i n (x - [x]) = c o s (x - [x])$ $x = {x} + [x]$ ${x} = f r a c t i o n a l p a r t f u n c t i o n$ $[x] = g r e a t e s t i n t e g e r f u n c t i o n$ $f r o m g r a p h i t i s s e e n t h a t i n [0, 2 π]$ $s i x (06) s o l u t i o n$
Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18

Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18

$g r a p h o f s i n {x}$ $s i n (x - [x]$
Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18

Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18

$g r a p h o f c o s {x}$ $g r a p h o f c o s (x - [x])$
Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18

Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18

$2 π = 2 \times 3.14 = 6.28$ $i n g r a p h i t i s s e e n t h a t f r o m x = 0 t o x = 6$ $t h e r e a r e s i x p o i n t w h e r e s i n {x} = c o s {x}$ $i n t e r s e c t s . s o s i x s o l u t i o n i n x (0, 2 π)$
Commented by vajpaithegrate@gmail.com last updated on 29/Nov/18

$tnq sir$
Commented by vajpaithegrate@gmail.com last updated on 29/Nov/18

$any alternate method,$
	Answered by mr W last updated on 29/Nov/18

	$l e t t = {x}$ $0 ⩽ t < 1$ $\sin t = \cos t$ $\Rightarrow \tan t = 1$ $\Rightarrow t = π / 4 = 0.785$ $\Rightarrow s o l u t i o n i s x = n + t w i t h n = 0, 1, 2, . . . .$ $i . e . x = 0.785, 1.785, 2.785, . . ., 5.785, 6.785, . . . . . .$ $2 π = 6.283 < 6.785$ $\Rightarrow 6 s o l u t i o n s w i t h i n [0, 2 π] :$ $x = 0.785, 1.785, 2.785, . . ., 5.785$
	Commented by vajpaithegrate@gmail.com last updated on 29/Nov/18

	$tnq sir$
	Commented by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18

	$e x c e l l e n t s i r . . .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum