Question

find solution in R in the interval )-π,π).
sin3x= -sin2x

Answer 1

use "sinc + sind" formula

Answer 2

SinC + SinD = 2Sin[(C+D)/2]Cos[(C-D)/2]

Answer 3

sin3x= -sin2x

sin3x + sin2x = 0

Answer 4

apply the formula now

Answer 5

but than what am goona do later

Answer 6

yeah lets see...
first, wat do u get after applying the formula ?

Answer 7

sin3x= -sin2x

sin3x + sin2x = 0

2sin(5x/2) cos(x/2) = 0

Answer 8

right ?

Answer 9

wait
am trying to get

Answer 10

take ur time :)

Answer 11

2sin(5x/2) cos(x/2)=0!!!!

Answer 12

yes !

Answer 13

can u explain more

Answer 14

sure :)
next :-

2sin(5x/2) cos(x/2)=0

sin(5x/2) = 0 OR cos(x/2) = 0

Answer 15

you need to solve both equations okay ?

Answer 16

yess

Answer 17

2sin(5x/2) cos(x/2)=0

sin(5x/2) = 0 OR cos(x/2) = 0

\(\large \frac{5x}{2} = \sin^{-1}0\) OR \(\large \frac{x}{2} = \cos^{-1}0\)

Answer 18

sin = 0 for what angels ?

Answer 19

kp

Answer 20

whut.. ?

Answer 21

x=kπ

Answer 22

yes, sin(x) is 0, whenever x = kpi

Answer 23

2sin(5x/2) cos(x/2)=0

sin(5x/2) = 0 OR cos(x/2) = 0

\(\large \frac{5x}{2} = \sin^{-1}0\) OR \(\large \frac{x}{2} = \cos^{-1}0\)

\(\large \frac{5x}{2} = k \pi\) OR \(\large \frac{x}{2} = ?????\)

Answer 24

wat about cos ?

cos = 0 for what angles ?

Answer 25

x=,π/2+k,π right!!

Answer 26

yup,
cos(x) = 0, when x = pi/2 + kpi

Answer 27

2sin(5x/2) cos(x/2)=0

sin(5x/2) = 0 OR cos(x/2) = 0

\(\large \frac{5x}{2} = \sin^{-1}0\) OR \(\large \frac{x}{2} = \cos^{-1}0\)

\(\large \frac{5x}{2} = k \pi\) OR \(\large \frac{x}{2} = \frac{\pi}{2} + k \pi\)

Answer 28

so, the general solutions are :-

\(\large \frac{5x}{2} = k \pi\) OR \(\large \frac{x}{2} = \frac{\pi}{2} + k \pi\)

Answer 29

thank uu :)

Answer 30

we're not done yet, we need to find "particular solutions" in the interval -pi and pi

Answer 31

so, the general solutions are :-

\(\large \frac{5x}{2} = k \pi\) OR \(\large \frac{x}{2} = \frac{\pi}{2} + k \pi\)

\(\large x = \frac{2}{5}k \pi\) OR \(\large x = \pi + 2k \pi\)

Answer 32

above is the general solution,
to get particular solutions in interval (-pi, pi) :-
put k = -2, -1, 0, 1, 2... and pick the x values that are between -pi and pi

Answer 33

yess i know how

Answer 34

you should get below solutions :-
\(\large \frac{-4\pi}{5}, \frac{-2\pi}{5}, 0, \frac{2\pi}{5} , \frac{4\pi}{5}\)

Answer 35

incase if u want to check ur answer... :)

Answer 36

:) (y)

Answer 37

u may check wid wolfram also :
http://www.wolframalpha.com/input/?i=sin%283x%29%3D+-sin%282x%29%2C+-pi%3Cx%3Cpi

Answer 38

why nott if i want help can ask u again????

Answer 39

sure :))