"What is the value of cos⁡π4" was answered by our experts

High School
Geometry
Trigonometry
Trigonometric Functions

William Collins

Answered question

2021-12-23

What is the value of

\cos \frac{π}{4}

Answer & Explanation

intacte87

Beginner2021-12-24Added 42 answers

Use the Unit Circle

\cos \frac{π}{4} = (\frac{1}{\sqrt{2}}) = \frac{\sqrt{2}}{2}

Jack Maxson

Beginner2021-12-25Added 25 answers

It is possible to find the exact value of

\cos \frac{π}{4}

by constructing a right triangle with one angle set to

\frac{π}{4}

radians.

\frac{π}{4} r a d = \frac{π}{4} r a d \times \frac{180 °}{π} \times r a d^{- 1} = 45 °

Now draw a right triangle with one of the acute angles set to 45 degrees. These two angles would be supplementary, and their sum would be 90 degrees. Thus, the other angle in this triangle would also be 45 degrees, making an isosceles right triangle.
Therefore,

\cos \frac{π}{4} = \cos (45) = \frac{a d j .}{h y p .} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}

user_27qwe

Skilled2021-12-30Added 375 answers

God, you saved me! Thank you

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Trigonometry

Didn't find what you were looking for?