Determine the cotangent of an angle on the unit circle ($ heta$)

The cotangent of an angle $ \theta $ on the unit circle is given by:

$ \cot( \theta ) = \frac{1}{\tan( \theta )} = \frac{\cos( \theta )}{\sin( \theta )} $

Let

The cotangent of an angle $ heta $ on the unit circle is:

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

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

$ sinleft( frac{pi}{4}
ight) = frac{sqrt{2}}{2} quad ext{and} quad cosleft( frac{pi}{4}
ight) = frac{sqrt{2}}{2} $

Then,

$ cotleft( frac{pi}{4}
ight) = frac{cosleft( frac{pi}{4}
ight)}{sinleft( frac{pi}{4}
ight)} = 1 $

The cotangent of $ heta $ on the unit circle is:

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

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

$ cotleft( frac{pi}{4}
ight) = 1 $

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