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Find the exact value of cos pi/12 using half angle identity. simplify,including
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:
3 years ago.
Category:
PreCalculus
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Expert:
Ryan
replied 3 years ago.
Hi,
Thank you for using JustAnswer.
The halfangle 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,
Ryan
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Customer:
replied 3 years ago.
which is the final answer?
Expert:
Ryan
replied 3 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,
Ryan
Ask Your Own PreCalculus Question
Customer:
replied 3 years ago.
here is an example they game me with the answer.
sin 7pi/12 = sqrt 2 + sqrt3/2
Expert:
Ryan
replied 3 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,
Ryan
Ryan, Engineer
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