Question

Find all solutions to the equation.

7 sin^2x - 14 sin x + 2 = -5

Answer 1

I have no clue on what to do....

Answer 2

Well if we make sin(x) =y then we can simplify this statement

Answer 3

\[\Large 7(y^2)-14(y)+2=-5\]

Answer 4

Okay, question. Why did you make sin(x)=y?

Answer 5

If you move the -5 you now have it set to 0 \[\Large 7(y^2)-14(y)+7=0\]

Answer 6

Oh i made it equal yo y because its much simpler to work with, just as long as we put it back at the end, there's no rules saying you can't do it, its really substitituion

Answer 7

\[7\sin ^{2}(x) - 14\sin(x) + 2 = -5\]
\[7\sin ^{2}(x) - 14\sin(x)= -7\]
\[-\sin ^{2}(x) + 2\sin(x) = 1\]
\[-\sin ^{2}(x) + 2\sin(x) - 1 = 0\]
\[(-\sin(x) + 1)(\sin(x) - 1)\]

Answer 8

Oh i made it equal to y because its much simpler to work with, just as long as we put it back at the end, there's no rules saying you can't do it, its really substitituion

Answer 9

How did you get -sin^2x+2sinx=1?

Answer 10

Divide by -7

Answer 11

If you can't visually do what he's doing, he's treating sin(x) like it was y by factoring it like that but some ppl can't do that so they can use the sub. method, anyways Im going to continue my explanation

Answer 12

OH BY 7

Answer 13

Yup

Answer 14

I'm confused on how you factored it

Answer 15

oh just kidding

Answer 16

Dividing both sides by 7 you get now \[\Large y^2-2y+1=0~~~~~~~~(y-1)^2=0\]

Answer 17

I understand it now! Thank you all(:

Answer 18

You're welcome

Answer 19

sqrt both sides:
y-1=0
replacing y with sin(x) again

sin(x)-1=0
sin(x)=0



YW

Answer 20

-sin(x) = -1
sin(x) = 1

sin(x) = 1
-2pi <= x <= 2pi

x = pi/2

Answer 21

sqrt both sides:
y-1=0
replacing y with sin(x) again

sin(x)-1=0
sin(x)=1

And it asked for all solutions so it wouldn't be in the interval -2pi<x<2pi it woul be

x= pi/2+2pi(n)

where n is any intger

YW

Answer 22

Well yea, if you included co terminal angles