Find tan θ if cos θ = one divided by four and sin θ < 0

In this case we have:

cos θ = 1/4

Whose possible solutions are:

θ = 2 * pi * n - Acos (1/4)

θ = 2 * pi * n + Acos (1/4)

Where,

n belongs to the natural numbers.

As sin θ <0 then the solution is:

θ = 2 * pi * n - Acos (1/4)

For n = 1 we get:

θ = 4.965069236 radians

Thus:

tan θ = tan (4.965069236) = - 3.872983346

Answer:

tan θ = - 3.872983346