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

We will use the concept of trigonometry to find the value of tan θ.

## Answer: If cos θ = one divided by four and sin θ < 0 then, tan θ = - √15

Let us see how we will use the concept of trigonometry to find the value of tan θ.

**Explanation**:

It is given that cos θ = one divided by four and sin θ < 0.

i.e, cos θ = 1 / 4 and sin θ < 0

Hence, θ will be an element of the fourth quadrant that is 3π / 2 < θ < 2π.

Now, let us consider a right-angled triangle with hypotenuse is 4 and base is 1 unit.

Thus, cos θ = 1 / 4 [ Since, cos θ = Base / Hypotenuse]

If the hypotenuse is 4 and the base is 1 unit, the perpendicular will be √15 units. ( By Pythagoras theorem.)

Now, tan θ = Perpendicular / Base