calculate cot(pi/4)

The cotangent is read as $\cot \left(u\right)=\frac{\cos \left(u\right)}{\sin \left(u\right)}$, on each interval where $\sin \left(u\right)\ne 0$

Let's calculate: $\frac{\cos \left(\frac{\pi }{4}\right)}{\sin \left(\frac{\pi }{4}\right)}$

ⓘ The cosine is the x-coordinate (horizontal axis) of the point reached on the unit circle after a rotation of $\frac{\pi }{4}$ radians from the horizontal axis pointing to the right, this is a remarkable value: $\cos \left(\frac{\pi }{4}\right)$ = $\frac{\sqrt{2}}{2}$■The sine is the y-coordinate (vertical axis) of the point reached on the unit circle after a rotation of $\frac{\pi }{4}$ radians from the horizontal axis pointing to the right, this is a remarkable value: $\sin \left(\frac{\pi }{4}\right)$ = $\frac{\sqrt{2}}{2}$

$\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}$

ⓘ The original denominator must remain nonzero. The fraction is simplified by dividing the numerator and the denominator by their common factor $\frac{\sqrt{2}}{2}$: $\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}$ = $1$

▶Result:   $1$