Help with circular funtions

sinθ=   y/ r = a / 1 = a

cosθ =  x / r

And

1 - sin^2 θ  =  1 - a^2  = cos^2 θ

So

cos θ  =  ± √ [ 1 - a^2 ]

And since  tanθ<0   = sinθ / cosθ = a / cosθ and a > 0.....this angle is in the second quadrant.....so the cosine is negative

So

cos θ  =   - √ [ 1 - a^2 ]