# If sin θ = 1 over 3 and tan θ < 0, what is the value of cos θ?

We will use the concept of trigonometry in order to find the value of cos θ.

## Answer: cos θ = - 2 √2 / 3

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

**Explanation:**

It is given that sin θ = 1 / 3

On squaring both sides we get

sin^{2} θ = 1 / 9

We know that cos^{2} θ + sin^{2} θ = 1

Hence, on substituting the value of sin θ in sin^{2} θ = 1 - cos^{2} θ, we get

1 - cos^{2} θ = 1 / 9

cos^{2} θ = 8 / 9

cos θ = 2 √2 / 3 or - 2 √2 / 3

Now it is also given that tan θ < 0 hence, cos θ < 0