Question

How do you calculate \[\sec 45^\circ \]?

Answer 1

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, \[\cos 45^\circ = \dfrac{1}{{\sqrt 2 }}\]
Also, we know that, \[\sec \theta = \dfrac{1}{{\cos \theta }}\]
Hence, \[\sec 45^\circ = \dfrac{1}{{\dfrac{1}{{\sqrt 2 }}}} = \sqrt 2 \approx 1.414\]

Note: In the given question, we had to find the value of three trigonometric functions for an equal angle. We did that by using the appropriate formulae. It is important to remember that after calculating the values, if we are given a negative angle, we need to account that. Also, the point where a lot of students make a mistake is not rationalizing the denominator of the calculated value – if the denominator is irrational, it is to be made rational by rationalizing it.