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

To find the cotangent of $\theta = \frac{\pi}{4}$ on the unit circle:

The cotangent function is given by:

$\cot \theta = \frac{1}{\tan \theta}$

Since $\tan \theta = \frac{\sin \theta}{\cos \theta}$, we first find the values of $\sin \theta$ and $\cos \theta$. For $\theta = \frac{\pi}{4}$:

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

Then:

$\tan \frac{\pi}{4} = \frac{\sin \frac{\pi}{4}}{\cos \frac{\pi}{4}} = 1$

Thus, the cotangent is:

$\cot \frac{\pi}{4} = \frac{1}{\tan \frac{\pi}{4}} = 1$

So, the answer is:

$\cot \frac{\pi}{4} = 1$

To determine the cotangent of $ heta = frac{pi}{4}$ on the unit circle:

Recall the cotangent identity:

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

For $ heta = frac{pi}{4}$, the values of $cos heta$ and $sin heta$ are:

$cos frac{pi}{4} = frac{sqrt{2}}{2}$ and $sin frac{pi}{4} = frac{sqrt{2}}{2}$

Therefore,

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

Thus,

$cot frac{pi}{4} = 1$

To find $cot frac{pi}{4}$ on the unit circle:

Use:

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

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

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

So:

$cot frac{pi}{4} = 1$

Start Using PopAi Today