Math Doubts

$\sec{45^\circ}$ value

Exact value

$\sec{45^\circ} \,=\, \sqrt{2}$

Introduction

The value of the secant in a forty five degrees right triangle is called the secant of angle forty five degrees.

According to the sexagesimal system, the angle forty five degrees is mathematically written as $45^\circ$ and the sec of $45$ degrees is written as $\sec{45^\circ}$ in mathematical form.

Radical form

The exact value of trigonometric function secant for a standard angle $45$ degrees is an irrational number and it is equal to the square root of two.

$\sec{(45^\circ)}$ $\,=\,$ $\sqrt{2}$

Decimal form

In decimal form, the sec $45$ degrees value is obtained as an irrational number with infinitely extended digits and its approximate value is equal to $1.4142$.

$\sec{(45^\circ)}$ $\,=\,$ $1.4142135624\ldots$

$\implies$ $\sec{(45^\circ)}$ $\,\approx\,$ $1.4142$

sec 45 degrees value

Other forms

Alternatively, the secant of $45$ degrees is written in trigonometry in two different forms.

Circular system

According to the circular system, the secant of angle $45$ degrees is written as secant of pi divided by four. The exact value of sec $\pi$ divided by $4$ is equal to $\sqrt{2}$ and its approximate value in decimal form is $1.4142$.

$\sec{\Big(\dfrac{\pi}{4}\Big)}$ $\,=\,$ $\sqrt{2}$ $\,\approx\,$ $1.4142$

Centesimal system

In the same way, the sec of standard angle $45$ degrees is written as sec of fifty gradians as per centesimal system. So, the exact value of sec $50$ grades is equal to the square root of $2$ and its value in decimal form is $1.4142$ approximately.

$\sin{(50^g)}$ $\,=\,$ $\sqrt{2}$ $\,\approx\,$ $1.4142$

Proof

Learn how to find the secant of angle $45$ degrees value as the square root of two by constructing a right angle with angle of $45^\circ$.

Math Doubts

A best free mathematics education website that helps students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved