Question

Find tan θ if sec θ = (sqrt26)/5 and sin θ < 0.

Answer 1

\[\tan\theta = \frac{\sin\theta}{\cos\theta}\]
\[\sec\theta = \frac{1}{\cos\theta}\]

Answer 2

I got cosθ= (5sqrt26)/26

Answer 3

also you can form a triangle from the secant ratio since:
\[\sec\theta = \frac{hyp}{adj}\]

Answer 4

since the tan requires the opposite side:
\[\tan\theta = \frac{opp}{adj}\]
you should solve missing side with pythagorean

Answer 5

So tanθ= 1/5 ?

Answer 6

right.

Answer 7

do the other questions your working on ask you to find an angle? if so i think that's why they give you: sin θ < 0

Answer 8

but in this context it appears to be extra information.

Answer 9

Well 1/5 isn't an option as an answer, but - 1/5 is...

Answer 10

@Mathmuse

Answer 11

since sin(theta) < 0, cos(theta) > 0 and tan = sin/cos, this means that tan(theta) is negative

Answer 12

Thank you @jim_thompson5910 !

Answer 13

np