Question

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

Answer 1

just apply the quadratic formula with ax^2 + bx + c = 0....

Answer 2

yep, so just take the -5 to the other side, and let sin(x)=s
you get
7s^2-14s+7=0
you can divide through by 7 to simplify it
then just apply the quadratic formula as above
just make sure in your solutions you substitute back in s=sin(x)

so you'll get like s= blah
which then you need to solve as it would be
sin(x)=blah
so x=sin^(-1) (blah)

Answer 3

yup

Answer 4

@sarahusher can you be more specific on the blah ?

Answer 5

okay so you'll get
(s^2)-2s+1=0
factorise and solve for s
(s-1)(s-1)=0

s=1 (repeated)
sin(x)=1
solve for x