Question

Find all solutions to the equation. 7 sin^2x - 14 sin x + 2 = -5

Answer 1

let sinx = y \[\huge\rm 7y^2-14y+2=-5\]
now you have quadratic equation
set it equal to zero (move -5 to the left side)

Answer 2

so \[7y ^{2}-14y+7=0\]?

Answer 3

yes right now can you solve for y ?

Answer 4

\[\frac{ 14+-\sqrt{196-4(7)(7)} }{ 2(7) }\]

Answer 5

oh wait you can take out the common factor

Answer 6

\[\huge\rm 7y ^{2}-14y+7=0\] what is gcf ?

Answer 7

7 so \[\frac{ 2+-\sqrt{4-4} }{ 2 }\]

Answer 8

right!

Answer 9

so \[\frac{ 2 }{ 2 }\]

Answer 10

then I find where that happens on the unit circle, right?

Answer 11

but it simplifies to \[\frac{ 1 }{ 1 }\]

Answer 12

yes right so \[\large\rm \frac{ 2 +0 }{ 2} ~and~ \frac{ 2-0 }{ 2 }\]
both equal to one
y= 1 now you can replace y with sinx
sin x =1 sin x =1

Answer 13

so \[\frac{ \pi }{ 2 }\]

Answer 14

right?

Answer 15

find `all solution`

Answer 16

wait do you need in radians or degree ?

Answer 17

so
3pi/2
5pi/2
7pi/2
etc.
?

Answer 18

radians

Answer 19

yes pi /2 is right !

Answer 20

is 3pi/2 right?

Answer 21

sinx = positive one

Answer 22

oh right
so is 5pi/2 right?

Answer 23

so like pi/2
5pi/2
9pi/2
etc.

Answer 24

right?

Answer 25

yes 5pi/2 can be the solutions

Answer 26

Ok, thanks!

Answer 27

but remember sinx =1 (multiplicity of 2)(sinx= 1 , sinx =1)

Answer 28

np good job!

Answer 29

OK!