Find the cotangent of $ frac{pi}{4} $ on the unit circle.

To find the cotangent of $ \frac{\pi}{4} $ on the unit circle, we use the definition of cotangent in terms of sine and cosine.

$ \cot \theta = \frac{\cos \theta}{\sin \theta} $

For $ \theta = \frac{\pi}{4} $, both $ \sin \frac{\pi}{4} $ and $ \cos \frac{\pi}{4} $ are $ \frac{\sqrt{2}}{2} $.

Therefore,

$ \cot \frac{\pi}{4} = \frac{\cos \frac{\pi}{4}}{\sin \frac{\pi}{4}} = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1 $

The cotangent of $ \frac{\pi}{4} $ is 1.

To determine the cotangent of $ frac{pi}{4} $ on the unit circle, we start by using the cotangent definition:

$ cot heta = frac{cos heta}{sin heta} $

Given $ heta = frac{pi}{4} $, the values are $ cos frac{pi}{4} = frac{sqrt{2}}{2} $ and $ sin frac{pi}{4} = frac{sqrt{2}}{2} $.

Hence,

$ cot frac{pi}{4} = frac{cos frac{pi}{4}}{sin frac{pi}{4}} = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1 $

So, the cotangent of $ frac{pi}{4} $ is 1.

To find $ cot frac{pi}{4} $:

$ cot heta = frac{cos heta}{sin heta} $

For $ heta = frac{pi}{4} $:

$ cot frac{pi}{4} = frac{cos frac{pi}{4}}{sin frac{pi}{4}} = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1 $

Therefore, $ cot frac{pi}{4} = 1 $.

Start Using PopAi Today