Question

Find all solutions to the equation.

7 sin2x - 14 sin x + 2 = -5

Answer 1

@dan815 @surjithayer @cwrw238

Answer 2

simplify the equation to get sin2x-2sinx+1=0

Answer 3

you know the formula for sin2x?

Answer 4

I have a cheet sheet for formulas and identities but not on this computer

Answer 5

sin2x =2sinx.cosx

Answer 6

equation becomes 2sinx.cosx-2sinx+1=0

Answer 7

i think it should be sin^2x

Answer 8

Oh yes your right @surjithayer

Answer 9

then its more easy i guess.

Answer 10

Okay so how do I start?

Answer 11

\[\sin ^{2}x-2\sin(x)+1=0\]

Answer 12

replace sin x by t just for solving purpose.

Answer 13

How did you get to that?

Answer 14

the above equation?

Answer 15

Yes

Answer 16

take -5 from right to left side
which makes in 7sin^2x-14sinx+7=0

Answer 17

Oh! I see it

Answer 18

now replace sinx by t for solving.
\[t ^{2}-2t+1=0\]

Answer 19

now solve for t.
i hope you know how to factorise.

Answer 20

So i believe t would equal 1

Answer 21

yea good.
now,
\[t=1\]
\[sin(x)=1\]

Answer 22

npw for what value of x sin x shouldbe equal to 1?

Answer 23

Im not sure what you mean

Answer 24

I may be over thinking it...

Answer 25

we replaced sin x by t?

Answer 26

right

Answer 27

so if t=1 sin x should also be equal to 1

Answer 28

right

Answer 29

now for what degree sin is 1?

Answer 30

let me tell you the answer.
sin(90)=1
sin(x)=1
so x=90.

Answer 31

or you can say (2n+1)*90

Answer 32

OH, i did over think it ! Great, I got it. Thanks!!

Answer 33

anytym.