Question

Find all values of x such that sin (2x) = sin (x) and 0 < x < 2\(\pi\)

Answer 1

sin2x = sinx

2sinxcosx = sinx

sinx(2cosx-1) = 0

Answer 2

use zero product property

Answer 3

hmm so you have sinx = 0 and cosx = 1/2

Answer 4

can u get that from a graph?

Answer 5

can you?

Answer 6

yes work it

Answer 7

anyway...that's 2 roots down...how about the three others?

Answer 8

i think it is the easier way since sin(2x) have period of pi u can graph both graph and see the common points

Answer 9

graphing sinusoidal functions? seems tedious

Answer 10

@ganeshie8 do you know how to get the three other roots of this?

Answer 11

hmm seems like he doesn't. he ran away =_= lol

Answer 12

sinx(2cosx-1) = 0

sinx = 0 ; cosx = 1/2

x = 0, pi ; x = pi/3

Answer 13

We're done. since you want to find roots within \((0, 2 \pi) \)

Answer 14

btw 0 wont work. so you would have oly 2 roots x = pi, pi/3

Answer 15

this is the way that i know the graphs meet in 0,pi and 2pi
but i dont know why i got a different answer ro @ganeshie8