Question

What is the correct definition for cot theta?

Answer 1

The correct answer is:

cot θ = (cos θ)/(sin θ).

Explanation:

We know that the tangent ratio is opposite/adjacent (O/A).

The ratio for sine is opposite/hypotenuse (O/H), and the ratio for cosine is adjacent/hypotenuse (A/H).

If we divide these two,

$\frac{\text{O}}{\text{H}}\div \frac{\text{A}}{\text{H}} \\ \\=\frac{\text{O}}{\text{H}} \times \frac{\text{H}}{\text{A}}=\frac{\text{OH}}{\text{HA}} \\ \\=\frac{\text{O}}{\text{A}}$

This is the same as the ratio for tangent, so we know that

tan θ = (sin θ)/(cos θ).

Since cot θ = 1/(tan θ), we now have

$\cot \theta = \frac{1}{\frac{\sin \theta}{\cos \theta}} \\ \\=1 \div \frac{\sin \theta}{\cos \theta}=1 \times \frac{\cos \theta}{\sin \theta} \\ \\=\frac{\cos \theta}{\sin \theta}$

Answer 2

The correct definition for cot theta is (cos theta)/(sin theta). Cotangent (in a right-angled triangle) the ratio of the side (other than the hypotenuse) adjacent to a particular acute angle to the side opposite the angle. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.