Question

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

Answer 1

If sin < 0 and sec > 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.