Suppose that cot(𝜃)=𝑐 and 0<𝜃<𝜋/2. What does cos(𝜃) equal in terms of 𝑐?

Answer 1

cotθ = sinθ / cosθ

For 0 < θ < π/2, we can use

sin²θ + cos²θ = 1

To solve for sinθ,

sinθ = sqrt(1 - cos²θ)

We then have

sqrt(1 - cos²θ) / cosθ = c

And this can be solved for cosθ