We know that
sin(-θ) = - sinθ
and that
tanθ = sinθ / cosθ
Then
sin(-θ) = - sinθ = 1/5
↓
sin(θ) = - 1/5
We want to find cosθ. Using the second formula we have that
cosθ = sinθ / tanθ
We replace sin(θ) = - 1/5 and tanθ =√6/12:
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