Question

Find tan θ if cos θ =1/4 and sin θ < 0.

Answer 1

according to the question, do you know what quadrant theta is in?

Answer 2

no

Answer 3

notice cosine = 1/4, a positive value,
and you're given sin theta < 0, sine is negative...

do you know what quadrant gives a positive cosine and negative sine ?

Answer 4

II

Answer 5

no, no quadrant II.
cosine is the x coordinate, sine is the y coordinate.
what quadrant is the x is positive, y is negative ?

Answer 6

IV

Answer 7

yes..
so in your original problem, what sign will tangent of an angle have in quadrant IV?

Answer 8

-

Answer 9

no +

Answer 10

u got it right the first time.. tan will be negative in quadrant IV..
now, you need to solve this triangle for the missing side: