Question

Solve the equation for solutions in the interval [0, 2pi]

7 sin^2 x - 14 sin x + 4 = -3

Should I factor... Use the quadratic formula? I'm horrible at both, so I'm really lost.

Answer 1

This is known as a disguised quadratic. If we let y=sin(x), then can you tell me what your equation is in terms of y?

Answer 2

Umm... 7 y^2 - 14 y + 4 = -3? :P

Answer 3

right now add 3 to both sides so right hand side is 0

Answer 4

7 y^2 - 14 y + 7 = 0 Now I can factor it I think?

Answer 5

yes - first divide through by 7
then factor to give 2 binomials

Answer 6

y^2 - 2 y + 1 -> (y - 1)( y - 1) -> y - 1 = 0 -> y = 1 -> sin(x) = 1 -> x = pi/2?

Answer 7

good except there is one more value of in the given range

Answer 8

* value of x

Answer 9

Would it be 3pi/2? That's -1 on my unit circle, but it's still included?

Answer 10

no there isn't - sorry - only pi/2
i thought 3pi/2 - before i realised sine 3pi/2 = -1

Answer 11

Ooh okay. Thanks both of you for the help! :D

Answer 12

yw

Answer 13

i'm tired and losing concentration - time for bed!