Question

Find all solutions in the interval [0, 2π).

sin2 x + sin x = 0

Answer 1

We cannot have different angles when we solve for these. We have a 2x and an x, and we have to have them be the same. So what we want to do is use an identity on sin2x so we can get functions with only an angle of x. Do you know the double-angle formula for sin2x?

Answer 2

Is that:
\[\sin^2x\]
Or \[\sin2x\]

Answer 3

Yeah, completely different if thats supposed to be squared xD Which I kinda think it is.

Answer 4

yes, it is squared.

Answer 5

If it's squared then it's simple simple simple

Answer 6

Alrighty. Then this we would factor in the same way we would as if those sin(x)'s were just regular x's. We factor it just like we woudl this:
\[x ^{2}+x=0 \]

Answer 7

So if you know how to factor the above quadratic, then you can factor this sin^2x + sinx = 0 equation :3

Answer 8

2 sin(x/2) cos(x/2) (sin(x/2)+cos(x/2))^2 = 0

Answer 9

Why did we do that? All we need to do is factor it like a quadratic. Its done in the same fashion as something like this:
\[x ^{3}+x=x(x ^{2}+1)\]
Youd be doing that process with your equation :3

Answer 10

Oh. I tend to over think things...

Answer 11

Well, youre just not used to seeing a quadratic being with trig functions xD

Answer 12

Exactly.

Answer 13

Thats why trig is tricky. Nothing like all the tons of algebra we have to do to get here :p SO following the method I did above, think you can factor what we have with our sines?

Answer 14

Is this query cleared?

Answer 15

We're still working it xD

Answer 16

Any 'help' needed?

Answer 17

I dont believe so. Just waiting for her to respond to see where we might need to go from here.

Answer 18

xD

Answer 19

I'm lost, I don't know what factor.

Answer 20

to factor

Answer 21

Ah, okay. Well, akash is eager, lol.

Answer 22

Hopefully, Akash can make this problem a bit less complicated like the previous one.

Answer 23

Yeah, you have a hard time understanding me it seems. Im sure hell do much better than what I can do.

Answer 24

1 sec.

Answer 25

No, it's just that these problems are really difficult for me. Don't take it personally.

Answer 26

Guys chill out on that!! LOL

Answer 27

No, its not that I take it persoanlly, I just think I suck compared to everyone else. So usually once someone else joins in ont he problem I leave because Im just going to embarrass myself.

Answer 28

All you have to do is take
sin x(sin x + 1) = 0
Now either
sin x = 0
Or sin x = -1
So x can be
0' or 270'

Answer 29

Yeah, I really despise any type of conflict...

Answer 30

'LoveIsKey' after all

Answer 31

Which is why its usually best for me to leave when others come in and join. I tend to cause a lot of conflict and drama.

Answer 32

@Psymon You should not think like that. This is not the first time you have aided me in a math problem, you're amazing. Do not underestimate yourself !

Answer 33

PS. Psymon you have a score of 74 now!
PROOF THAT YOU DON'T SUCK!! :D

Answer 34

that means nothing, lol. It means I go to a lot of problems xD

Answer 35

LoL, No chill out on the 'Insulting yourself' XD :D
It is FUNNY

Answer 36

Okay, Not drifting away from the topic
@Loveiskey18
Did you understand what I did?

Answer 37

Lol, it what I always do xD

Answer 38

How did you get 270?

Answer 39

sin 270 is -1
That's how! :)

Answer 40

I'm just going to agree with you... -__-

Answer 41

Sin refers to y-coordinates. If you actually look at the circle and point our where 270 is....

Answer 42

Why why why???
Ask me if you have any question!!!!

Answer 43

Yeah! Psymon is right over there!

Answer 44

This sin, cos, tan stuff is the reason why I can not get an amazing score on my ACT . Why do we have them, because I am really going to use sin, cos and tan in my daily life.. :)

Answer 45

Well, a lot of people think math is a sin.

Answer 46

Try Learning all
cosine, sine and tangent values for
0, pi/2 , pi , 3pi/2 , 2pi radians!
It WILL help!! :D

Answer 47

And the people who love math say without geometry life is pointless.

Answer 48

Oh, the unit of Circle !

Answer 49

Lol There!!

Answer 50

@Loveiskey18 Did you get how I computed this though?

Answer 51

Yep yep. Absolutely. All the values on the unit circle refer to actual points on a graph. Sin(pi/6) is 1/2 because the y-coordinate, if you were to plot it, is 1/2!

Answer 52

Yes, somewhat. Laughing out loud

Answer 53

What is the other 'Somewhat' you do not get?

Answer 54

Oh, I'm just wondering how we are going to get from 270 to this:

x = 0, π, pi divided by three, five pi divided by three

x = 0, π, pi divided by three, two pi divided by three

x = 0, π, four pi divided by three, five pi divided by three

x = 0, π, three pi divided by two.

That is the somewhat that I do not get.

Answer 55

Btw I forgot to mention even
180 degrees would be a value because
sin 180 or sin pi is 0 :D
So it should be Option D.!!! :D

Answer 56

Makes me think of the little cartoons in my math book: