The tangent function is the ratio of the sine function to the cosine function.
This can also be written as: \(tan(x)= \frac{sin(x)}{cos(x)}\)
Consider the location of \(90\)˚ on the unit circle: it is at the point \((0,1)\).
This means that \(sin(90\)˚\()=1\) and \(cos(90\)˚\()=0\).
According to the relationship of sine and cosine to tangent that we defined earlier, we see that \(tan(90\)˚\()=\frac{1}{0}\).
However, it is impossible to divide by \(0\). Thus, the tangent of\(90\)˚ is undefined.
Another way to think of tangent is as the slope of the line at the point on the unit circle. Since \(90\)˚ is straight up, we know that the slope of a vertical line is undefined.
