Question

Solve for theta
Sin theta = -1/2

Answer 1

After looking at the list of trigonometric identities, I can't seem to find a way to solve this. Is it solvable?

cos(θ)+sin(θ)=x.

cos⁡(θ)+sin⁡(θ)=x.

What if I added another equation to the problem:

−sin(θ)+cos(θ)=y,

−sin⁡(θ)+cos⁡(θ)=y,

where θθ is the same and yy is also known?

Thanks.

EDIT:

OK, so using the linear combinations I was able to whip out:

asin(θ)+bcos(θ)=x=a2+b2−−−−−−√sin(θ+ϕ),

asin⁡(θ)+bcos⁡(θ)=x=a2+b2sin⁡(θ+ϕ),

where ϕ=arcsin(ba2+b2√)=π4ϕ=arcsin⁡(ba2+b2)=π4 (as long as a≥0a≥0)

Giving me:

x=sin(θ+π4) and arcsin(x)−π4=θ.

hope this answer helpful u

Answer 2

Answer:

Step-by-step explanation: