Question

If 2sin(theta) = 2 - cos theta ,find sin theta

Answer 1

You could square both sides. First get the cosine alone, that way you can use the identity. \[\large 2\sin \theta -2 = - \cos \theta \]then square both sides \[\large (2\sin \theta -2)^2 = \cos^2 \theta \] then you can replace cos^2 theta.
\[\large (2\sin \theta -2)^2 = 1- \sin^2 \theta\]Now expand the left, and get it equal to zero, and it should be possible to factor like a quadratic.

Answer 2

2sin^2 theta + 4 - 2(2sin(theta)(2)

Answer 3

Check your math.

Answer 4

4sin^2 theta + 4 - 2(2sin(theta)(2)

Answer 5

idk what 2(2sin(theta)(2) is meant to be but clean it up.

Answer 6

8 sin theta?

Answer 7

Then write 8 sin theta...

Answer 8

And you're missing an equals sign.
\[\large 4\sin^2 \theta -8 \sin \theta +4 = 1- \sin^2 \theta\]

Answer 9

Do I have to move the - sin^2 theta from the RHS to the LHS

Answer 10

Yes, get it equal to zero.

Answer 11

\[5 \sin^2 \theta - 8 \sin \theta + 3 = 0\]

Answer 12

Now factor as if it was 5x^2 - 8x +3 = 0

Answer 13

-5 and 3 ?

Answer 14

5x^2 - 5x - 3x +3 = 0

Answer 15

5x(x-1)-3(x-1)
(5x-3)(x-1)

Answer 16

x = 3/5 ot x = 1

Answer 17

or*

Answer 18

Don't forget it's not actually 5x^2 - 8x +3 = 0...

Answer 19

I do know that.
So now theta = 3/5or 1 ,right?

Answer 20

or sin theta = 1
theta = 90

Answer 21

Look at the question again, you aren't asked for theta, you're asked for sine theta.

Answer 22

3/5 and 1 can be the values of sin theta

Answer 23

Remember you replaced x with sin theta, so de-replace and you have sin theta = 3/5 and sin theta = 1