Find tan θ if sec θ = square root of ten divided by three and sin θ < 0.

If sin 0, theta must be located in quadrant IV where tan < 0

Use x for theta

So to compute for this:Sec x = √10/3

cos x = 3 / √10

sin x = - √ (1-cos^2x)

= - √ (1 - (9/10))

= - √ (1/10)

= - 1/√10

tan x = sin x/cos x

=-1/3 is the answer for this problem.