Question

How do you find exact value of `cos (pi/ 4)`?

Answer 1

Let's first convert to degrees.

Explanation:

The conversion ratio between degrees and radians is `180/pi`.

`pi/4 xx 180/pi = 45^@`

Now, we must think of the special triangle that contains a `45^@` angle. This would be the following triangle.

The definition of cos is adjacent/hypotenuse. Therefore, our ratio is `1/sqrt(2)`. However, often, teachers want the denominator to be rationalized, or be a rational number. Since the expression is a monomial, we multiply the entire expression by the denominator.

`1/sqrt(2) xx sqrt(2)/sqrt(2)`

=`sqrt(2)/2`

Hopefully this helps.