anonymous
  • anonymous
use double angle formula to find the exact value of 2cos^2(3pie/8)-1
Mathematics
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anonymous
  • anonymous
use double angle formula to find the exact value of 2cos^2(3pie/8)-1
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Okay...
anonymous
  • anonymous
Use the fact that\[\cos{2 \theta}=\cos^2 \theta -\sin^2 \theta=2\cos^2 \theta -1\]
anonymous
  • anonymous
For\[\theta = \frac{3\pi}{8}\]\[\cos 2 \theta =\cos \frac{3 \pi}{4}=\cos^2 \frac{3 \pi}{8}-1\]The right-hand side is your expression. Now

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anonymous
  • anonymous
\[\frac{3\pi}{4}\] lies in the second quadrant where cosine is negative. 3pi/4 is equivalent to 135 degrees. The cosine of 135 degrees is equal to the the negative cosine of 45 degrees, which has an exact value of \[-\frac{1}{\sqrt{2}}\]
anonymous
  • anonymous
thank you!!!
anonymous
  • anonymous
become a fan! would love the points
anonymous
  • anonymous
what is the exact value of 2sin 157.5 cos 157.5
anonymous
  • anonymous
This is an example of double angle for sine.\[\sin 2 \theta = 2 \sin \theta \cos \theta\]Here theta is 157.5, so 2 x theta = 315 degrees. 315 = 360 - 45 This lies in the fourth quadrant where sine is negative. You have sin(315)=-sin(45)= -1/sqrt(2) again.
anonymous
  • anonymous
it says write the following expression as sin cos or tan of a double agent. then find the exact value

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