Question

Sin (4x) + sin(2x) =0

Answer 1

hint:
sin(4x) = sin(2*2x) = 2sin(2x)cos(2x)

Answer 2

Nope. Its spsssin 4x +sin2x=0

Answer 3

Sourwing, I know that but only there :(

Answer 4

Oh OK thanks

Answer 5

looks confusing where the powers and where the sin of (2x) and (4x)....

Answer 6

I changed it already @SolomonZelman

Answer 7

\(\LARGE\color{black}{ \sin (4x) + \sin(2x)=0 }\)
\(\LARGE\color{black}{ 2\sin (2x)\cos(2x)+ \sin(2x)=0 }\)
\(\LARGE\color{black}{ (2\cos(2x)+1)\times \sin(2x)=0 }\)

Answer 8

(zero product property)

Answer 9

Sorry, but i don't get it for the third line

Answer 10

I factored out of `sin(2x)`

Answer 11

Like, how did sin(4x) become2cos(2x)+1

Answer 12

sin(4x) became 2sin(2x)cos(2x)
using the sin(a+b) rule.

Answer 13

look how can you be at two things at once

Answer 14

??

Answer 15

look you hacker

Answer 16

But, isn't it it should become 4 cos^3 x sinx- 4sin^3 x cosx?

Answer 17

Solomon

Answer 18

would would sin(4x) become that?

Answer 19

Yeah,by using the gen. Add formula

Answer 20

\(\LARGE\color{black}{ \sin(4x)=\sin(2x+2x) }\)
\(\LARGE\color{black}{ \sin(4x)=\sin(2x)\cos(2x)+\sin(2x)\cos(2x) }\)
\(\LARGE\color{black}{ \sin(4x)=2\sin(2x)\cos(2x) }\)

\(\LARGE\color{black}{ \color{red}{ \sin(4x)}+\sin(2x)=0 }\)
\(\LARGE\color{black}{ \color{red}{ 2\sin(2x)\cos(2x)}+\sin(2x)=0 }\)

Good?

Answer 21

Yeah, and I can't seem to understand what to do after that

Answer 22

Thanks btw

Answer 23

Oh nvm, I understood it already, thanks Solomon!

Answer 24

Okay, and then you get,
\(\LARGE\color{black}{ 2\color{blue}{\sin(2x)}\cos(2x)+\color{blue}{\sin(2x)}=0 }\)

Answer 25

Factor it out of sin(2x). What do you get?

Answer 26

It will become (2cos (2x)+1)(sin(2x)=0

Answer 27

yes.

Answer 28

And then applying the zero product property, you get
`sin(2x)=0` or `2cos(2x)+1=0`

Answer 29

can you solve the sin(2x)=0 for x?

Answer 30

And now my problem is how to get the values for x

Answer 31

Sin (2x)=0 is x=0,180& 360 right?

Answer 32

oops I mean, x= 0,90,and 180?

Answer 33

yes, x=90 and 180.
so that the sin(2x) is sin(180) sin(360) as you have just fixed it... :)

Answer 34

and the second part,
`2cos(2x)+1=0` subtract 1 from both sides, divide both sides by 2
then tell me cos(a) for which value(s) of a is 1/2?

Answer 35

a= 60 and 120?

Answer 36

sure that cos(120) is 1/2?

Answer 37

I wouldn't say that.. lol

Answer 38

isn't it correct?
as when 2a= 120,240,480 and 600
and a now is 60,120,240 and 300?

Answer 39

nvm 480,600 and 240,300

Answer 40

I mean sin(2x)=1/2 is when x=30.

Answer 41

but isn't it that we are using the cos function?
and cos(2x)= -1/2

Answer 42

yeah, my bad cos.

Answer 43

cos(60)=1/2
so when 60 is 2x, then x is 30.

Answer 44

It was my bad that I typed sin when I mean cos -:(

Answer 45

it's ok, but is the values right? i mean 60 and 120 for a?

Answer 46

HINT: \(\large\color{black}{ 30 }\) degrees is \(\large\color{black}{ \pi/6 }\) .

Answer 47

we are doing the 2x, so
2x would be \(\large\color{black}{ \pi/3 }\)
(when x is \(\large\color{black}{ \pi/6 }\) )

Answer 48

but it is negative. so isn't it that 2x would be 120 and 240? because it is where cos is negative? :3

Answer 49

yes.

Answer 50

so it is 60 and 120?

Answer 51

yees

Answer 52

oh ok, thanks @SolomonZelman !!!

Answer 53

No problem.