$\csc{(45^°)}$ value

The value of cosecant function when angle of right triangle equals to $45^°$ is called cosecant of angle $45$ degrees. It is written as $\csc{(45^°)}$ or $\operatorname{cosec}{(45^°)}$ according to the sexagesimal system in mathematics.

$\csc{(45^°)} \,=\, \sqrt{2}$

The exact value of cosecant of angle $45$ degrees is $\sqrt{2}$ in fraction form. It is an irrational number and equal to $1.4142135624\ldots$ in decimal form but its approximate value is taken as $1.4142$ in mathematics. Actually, the value of $\csc{(45^°)}$ is generally called as trigonometric function or trigonometric ratio for standard angle.

Alternative form

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

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

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

Proof

You knew the exact value of cosecant of angle $45$ degrees in both fraction and decimal from and it is time to learn how to find the exact value of $\csc{\Big(\dfrac{\pi}{4}\Big)}$ in trigonometric mathematics.