Find the value of $cot( heta)$ in the unit circle where $ heta = 45^{circ}$.

Given $\theta = 45^{\circ}$ in the unit circle, we need to find $\cot(\theta)$.

First, recall that $\cot(\theta) = \frac{1}{\tan(\theta)}$.

At $\theta = 45^{\circ}$, $\tan(45^{\circ}) = 1$.

Therefore,

$ \cot(45^{\circ}) = \frac{1}{1} = 1 $

Hence, the value of $\cot(45^{\circ})$ is 1.

To find $cot(45^{circ})$ in the unit circle, we start by using the definition:

$cot( heta) = frac{cos( heta)}{sin( heta)}$.

At $ heta = 45^{circ}$, both $cos(45^{circ})$ and $sin(45^{circ})$ are $frac{sqrt{2}}{2}$.

Thus,

$ cot(45^{circ}) = frac{cos(45^{circ})}{sin(45^{circ})} = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1 $

So, $cot(45^{circ})$ is 1.

Using $cot( heta) = frac{1}{ an( heta)}$,

at $ heta = 45^{circ}$,

$ cot(45^{circ}) = frac{1}{1} = 1 $

Therefore, $cot(45^{circ})$ equals 1.

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