How do you find the value of \[\sec 90^\circ \]?

Hint: In the given question, we have been asked the exact value of a trigonometric ratio with a constant angle. By exact value, it means that if the value is in fractions, we have to convert it to decimals. This is achieved by dividing the numerator by the denominator. If the denominator is an irrational number, then we shift the irrational number to the numerator by rationalizing it.

Complete step-by-step answer:
We know, \[\sec \theta = \dfrac{1}{{\cos \theta }}\]
So, we write the value of cosine for those values and then divide them.
Now, \[\cos 90^\circ = 0\]
Hence, \[\sec 90^\circ = \dfrac{1}{0} = not{\rm{ }}\,defined\]
Hence, the value of \[\sec 90^\circ \] is not defined.

Note: We have to give care if the denominator is irrational, if it is then we have to rationalize. When we are rationalizing the denominator as it is the only place where we could make an error.