Question

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

2 sin^2x = sin x

Answer 1

x can be either 30 degrees or 150 degrees

Answer 2

you mean the unit circle right? I always have trouble with that

Answer 3

want me to show you how?

Answer 4

I'd love that! By the way this is a multiple choice question...so the answer looks like pi/2 , 3pi/2...like that...

Answer 5

Does that make it easier?

Answer 6

Oh and this is also the first time I've ever asked a question on this website so I'm really thankful for the help! ^-^

Answer 7

let a=sin(x)
you have
2a^2-a=0
a(2a-1)=0
so a=0 or a=1/2
so
sin(x) = 0 or sin(x) = 1/2
when does this happen?
well sin(x) = 0 when x is 0,pi, and 2pi but we don't include 2pi
sin(x) = 1/2 when x is pi/6 and 5pi/6
so
x=0,pi,pi/6,5pi/6

Answer 8

understand?

Answer 9

hmm I think so...I guess Death left...he was gonna help me with the unit circle. Can we try one more?

Answer 10

the unit circle is just memorization. You just need to know the basic angles.
and if you know sin(x) and cos(x) for 0,pi/3,pi/4,pi,6,and pi/2 you can get the rest real easy

Answer 11

http://www.youtube.com/watch?v=1-hrT1Ys390
this should help

Answer 12

7 sin^2x - 14 sin x + 2 = -5 ...but what if it isn't equal to 0?

Answer 13

what if x^2+3x=4?

Answer 14

you set it to zero right?

Answer 15

x^2+3x-4=0

Answer 16

so again let a=sin(x)
you have
7a^2-14a+7=0

Answer 17

do you understand what I did?

Answer 18

you replaced the sin with a to make it less confusing right?

Answer 19

ah! didn't mean tot write that
you cancelled the -5 by adding it to both sides which gave you the 7

Answer 20

right?