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Category: Pre-Calculus
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# Find the exact value of cos pi/12 using half angle identity?

### Resolved Question:

Find the exact value of cos pi/12 using half angle identity.
simplify,including any radicals. Use integers or fractions for any numbers in the expression.Rationalize all denominators.
Submitted: 4 years ago.
Category: Pre-Calculus
Expert:  Ryan replied 4 years ago.

Hi,

The half-angle identity for cosine is:

cos(a/2) = ±√(1 + cos a)/2

Using this:

cos(pi/12) = cos (pi/6 / 2) = ±√(1 + cos pi/6)/2 = ±√(1 + √3/2)/2 = ±√(1/2 + √3/4)

cos(pi/12) = ±√(2+√3) / √4

cos(pi/12) = ±(1/2)√(2+√3)

cos(pi/12) ≈ 0.9659

Please let me know if you need to match a specific answer choice like some of yesterday's problems.

Thanks.

Customer: replied 4 years ago.
Expert:  Ryan replied 4 years ago.

Hi,

That depends on if they are asking for a value or an expression.

If they want a value, then it is 0.9659, when rounded to four decimal places.

If they want an expression, then it could be ±√((1 + cos pi/6) / 2). In this case though, it would be helpful to see the answer choices that are available (if it is multiple choice).

Thanks.

Customer: replied 4 years ago.
here is an example they game me with the answer.
sin 7pi/12 = sqrt 2 + sqrt3/2
Expert:  Ryan replied 4 years ago.

Hi,

The answer for cos(pi/12) happens to be the same as the answer for sin(7pi/12).

It looks like this:

(The computer program might not care about the ± sign though...)

Thanks.