Question

Find all solutions to the equation.

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

Answer 1

start by setting it equal to 0

Answer 2

ok so it will be the same thing plus 7

Answer 3

Now, notice anything we can factor?

Answer 4

do i factor out the 7?

Answer 5

and why yes, yes you do

Answer 6

so it would be 7(sin^2x -2sinx +1)

Answer 7

and then do i factor the inside?

Answer 8

Yup :P

Answer 9

(sinx-1)^2?

Answer 10

correct, now set each equal to 0:
\[7=0\]
\[sinx-1=0\]

Answer 11

so solutions when sinx is 1? and what do i do with the 7?

Answer 12

From there you find where sinx is one on the unit circle

Answer 13

pi/2 and 3pi/2?

Answer 14

well pi/2 is right.
At 3pi/2 sin is -1

Answer 15

yeah i just saw that. lol thank you so much! so is it just the one?

Answer 16

Yup, and you are welcome :P