$\cos{(45^°)}$ value

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

$\cos{(45^°)} \,=\, \dfrac{1}{\sqrt{2}}$

The value of cos of angle $45$ degrees in fraction is $\dfrac{1}{\sqrt{2}}$ exactly. It is an irrational number and equal to $0.7071067812\ldots$ in decimal form. However, the approximate value of cos of $45$ degrees is taken as $0.7071$ in mathematics. In general, the value of $\cos{(45^°)}$ is called as trigonometric function or trigonometric ratio of standard angle.

Alternative form

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

$(1) \,\,\,$ $\cos{\Big(\dfrac{\pi}{4}\Big)}$ $\,=\,$ $\dfrac{1}{\sqrt{2}}$ $\,=\,$ $0.7071067812\ldots$

$(2) \,\,\,$ $\cos{(50^g)}$ $\,=\,$ $\dfrac{1}{\sqrt{2}}$ $\,=\,$ $0.7071067812\ldots$

Proof

Now, you know the exact value of cos of $45$ degrees in both fraction and decimal form and also know the approximate value. Now, you can learn how to derive the value of $\cos{\Big(\dfrac{\pi}{4}\Big)}$ in trigonometric mathematics.

Email subscription
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more
Follow us on Social Media
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.