$\sec{(45^°)}$ value

The value of secant function when angle of right triangle equals to $45^°$ is called secant of angle $45$ degrees. It is written as $\sec{(45^°)}$ as per sexagesimal system in mathematics.

$\sec{(45^°)} \,=\, \sqrt{2}$

The value of sec of angle $45$ degrees in fraction is $\sqrt{2}$ exactly. It is an irrational number and equal to $1.4142135624\ldots$ in decimal form but the approximate value of secant of angle $45$ degrees is considered as $1.4142$ in mathematics. Generally, the value of $\sec{(45^°)}$ is called as trigonometric function or trigonometric ratio for standard angle.

Alternative form

$\sec{(45^°)}$ is written in alternative form as $\sec{\Big(\dfrac{\pi}{4}\Big)}$ in circular system and also written as $\sec{(50^g)}$ in centesimal system.

$(1) \,\,\,$ $\sec{\Big(\dfrac{\pi}{4}\Big)}$ $\,=\,$ $\sqrt{2}$ $\,=\,$ $1.4142135624\ldots$

$(2) \,\,\,$ $\sec{(50^g)}$ $\,=\,$ $\sqrt{2}$ $\,=\,$ $1.4142135624\ldots$

Proof

You know the exact value of secant of angle $45$ degrees in both decimal and fraction from and it is time to learn how to evaluate the exact value of $\sec{\Big(\dfrac{\pi}{4}\Big)}$ in trigonometry.