Cotangent Calculator

About Cotangent Calculator

Cotangent is the reciprocal of tangent. cot(θ) = cos(θ)/sin(θ). cot(45°) = 1.

How to use this calculator

1. Enter the angle \(\theta\) in the calculator.
2. Choose the correct angle unit, degrees or radians.
3. Click calculate to get \(\cot(\theta)\).
4. Review the result and the step-by-step explanation if it is shown.

The formula explained

The cotangent formula computes the cotangent of an angle using either \(\cot(\theta)=\frac{1}{\tan(\theta)}\) or \(\cot(\theta)=\frac{\cos(\theta)}{\sin(\theta)}\). It gives the ratio that is the reciprocal of tangent.

• \(\theta\) = the angle you want to evaluate
• \(\tan(\theta)\) = the tangent of the angle
• \(\cos(\theta)\) = the cosine of the angle
• \(\sin(\theta)\) = the sine of the angle

Step by step method

1. Find the tangent, cosine, and sine of the angle if needed.
2. Use \(\cot(\theta)=\frac{1}{\tan(\theta)}\) or \(\cot(\theta)=\frac{\cos(\theta)}{\sin(\theta)}\).
3. Simplify the fraction to get the cotangent value.

Worked example

Problem. Find \(\cot(45^\circ)\).

1. Use the tangent value, \(\tan(45^\circ)=1\).
2. Apply the formula, \(\cot(45^\circ)=\frac{1}{\tan(45^\circ)}=\frac{1}{1}\).
3. So \(\cot(45^\circ)=1\).

Tips and common mistakes

• Cotangent is undefined when \(\sin(\theta)=0\), because division by zero is not allowed.
• Make sure your calculator is set to degrees or radians to match the angle you entered.

Frequently asked questions