find cos theta if cot theta is 1/3

Question

well im just looking for answer 

Answer 1

cotθ = cosθ / sinθ = cosθ / √(1 - cos²θ)

 

Let x = cosθ

 

1/3 = x / √(1 - x²)

 

1/9 = x² / (1 - x²)

 

(1/9)(1 - x²) = x²

 

You can see that a quadratic equation in x will come out of this.  Express it in standard form and then use the quadratic formula to find x.  Try to finish from here.