Question

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

Answer 1

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