Question

Solve the following equation on the interval [0,2pi).

sin x-2 sin x cos x = 0

Answer 1

how about factoring that sinx
what do get if you did

Answer 2

1-cos x?

Answer 3

where did sinx go
\[\sin x(1-2\cos x)=0\]

Answer 4

set EACH ONE EQUAL TO ZERO

Answer 5

and solve

Answer 6

let me see your work!

Answer 7

how did you get sin x (1-2cos x)=0?

Answer 8

i factored sinx my friend

Answer 9

wait did you subtract 2sin x from sin x?

Answer 10

no do you know how to factor?

Answer 11

Yeah I can factor, but I get confused with trigonometric functions

Answer 12

how do you factor \[x-2xy\]

Answer 13

say how would you factor?

Answer 14

I have no idea

Answer 15

you just said you know how to do it, but you only have issue with trig

Answer 16

that's not trig just a linear expression

Answer 17

I can factor equations like x^2+3x+3

Answer 18

well if you can factor that why can't you factor x-2xy? what is common btw x and -2xy?

Answer 19

the x's

Answer 20

yes so can we then factor the x's
and get x(1-2y)

Answer 21

if i factored x in the first i'm left with 1
if i factored x in the second term i'm left with -2y

Answer 22

sorry my net cut out

Answer 23

sin x=0 cosx= 1/2

Answer 24

0, pi, pi/6, 5pi/6 is what I got

Answer 25

show your work?

Answer 26

I just used the unit circle?

Answer 27

show the whole work my friend, you skipped many steps

Answer 28

sin x=0
1-2cosx=0
-2cosx=-1
cox x=1/2
?

Answer 29

yes and then?

Answer 30

I just used the unit circle, sinx=0 is at pi and 0 and cosx=1/2 is at pi/3 and 5pi/3

Answer 31

damn I messed it up lol

Answer 32

what about 2pi?

Answer 33

for sin

Answer 34

isn't zero as well

Answer 35

and it is pi/6 not pi/3 the first answer you provided was correct except that you missed 2pi

Answer 36

Yeah I got 0, 2pi I'm assuming because it's [0,2pi)?

Answer 37

oh it is open i didn't see that
then you are good

Answer 38

alright thanks, can you help me with one more?

Answer 39

sin(2x+pi/6)=1/2 no idea how to even begin

Answer 40

when does an angles give 1/2 when you sin it?
and is there and interval given (because you have to make sure the values are in that interval)

Answer 41

interval is [0,2pi) and pi/6 and 5pi/6

Answer 42

then 2x+pi/6=pi/6 or 2x+pi/6=5pi/6

Answer 43

solve for x

Answer 44

x=2 or x=4pi/3 ?

Answer 45

how come x=2?
2x=0 how did you get x=2?

Answer 46

I read it wrong, oops

Answer 47

so sin of 0 and sin of 4pi/3?

Answer 48

hmm no
x=0 and x=4pi/6=2pi/3

Answer 49

I thought 4pi was its own entity? I'm doing online math so I'm essentially teaching everything to myself so sorry for the lack of math experience

Answer 50

oh no problem
you did good you just didn't simplify nicely
5pi/6-pi/6 =4pi/6 not 4pi/3

Answer 51

so the next step would be to get the sin of both angles?

Answer 52

or the sin of 1/2?

Answer 53

you are done what else you want?
they asked you to find x and you found it??

Answer 54

why is the answer 0,pi/3,pi,4pi/3? I thought it was 2pi/3?

Answer 55

where did the pi/3 and 4pi/3 come from?