What is the tangent of 45 degrees on the unit circle?

The tangent of an angle in the unit circle is given by $ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} $.

For $ \theta = 45^{\circ} $ or $ \theta = \frac{\pi}{4} $ rad:

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

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

Therefore,

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

The tangent of an angle $ heta $ in the unit circle is defined as $ an( heta) = frac{sin( heta)}{cos( heta)} $.

For $ 45^{circ} $ or $ frac{pi}{4} $:

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

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

Thus,

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

For $ 45^{circ} $ or $ frac{pi}{4} $:

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

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