Marion needs to find the cosine of Pi over 12. If she knows that cos Pi over 6 = root 3 over 2, how can she use this fact to find the cosine of Pi over 12? What is her answer. Please explain and show your work
1
Expert's answer
2020-10-26T19:19:29-0400
Use double angle formula for cosine cos(2A)=2cos2(A)−1
So, the cosine of angle A can be written as,
2cos2(A)=1+cos(2A)
cos2(A)=21(1+cos(2A))
cos(A)=21(1+cos(2A))
Plug A=12π into the relation cos(A)=21(1+cos(2A)) to obtain,
cos(12π)=21(1+cos(2(12π)))
=21(1+cos(6π))
=21(1+23) .....plug cos(6π)=23
=21(22+3)
=41(2+3)
=212+3≈0.965926
Therefore, the cosine of 12π is cos(12π)=212+3≈0.965926
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