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

1 Answer
Noah G
Apr 4, 2016

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.

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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.

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