What is the value of $cot(45^circ)$ on the unit circle?

To find the cotangent of 45 degrees, we use the definition of cotangent on the unit circle:

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

For $\theta = 45^\circ$, we know that:

$\cos(45^\circ) = \frac{\sqrt{2}}{2}$

$\sin(45^\circ) = \frac{\sqrt{2}}{2}$

Therefore,

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

So, the value of $\cot(45^\circ)$ is 1.

The cotangent function is defined as the ratio of the cosine to the sine of an angle.

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

At $ heta = 45^circ$:

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

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

So, we calculate:

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

Thus, $cot(45^circ) = 1$.

The cotangent of 45 degrees is:

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

Given:

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

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

Thus:

$cot(45^circ) = 1$

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