Cos Pi/4: please explain how to obtain the exact value
- Thread starter gasper
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Re: Cos Pi/4
Memorization is the usual way on this one. It is likely you are expected to know just a few values. Generally, \(\displaystyle 0\), \(\displaystyle \frac{\pi}{6}\), \(\displaystyle \frac{\pi}{4}\), \(\displaystyle \frac{\pi}{3}\), and \(\displaystyle \frac{\pi}{2}\). The last two may be redundant, depending on what identities and awareness you possess.
Memorization is the usual way on this one. It is likely you are expected to know just a few values. Generally, \(\displaystyle 0\), \(\displaystyle \frac{\pi}{6}\), \(\displaystyle \frac{\pi}{4}\), \(\displaystyle \frac{\pi}{3}\), and \(\displaystyle \frac{\pi}{2}\). The last two may be redundant, depending on what identities and awareness you possess.
skeeter
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Re: Cos Pi/4
sketch an isosceles right triangle. the two equal acute angles are both 45 degrees = pi/4 radians. if the two equal sides have length "a", the hypotenuse has length "a*sqrt(2)".
cos(pi/4) = (adjacent side)/(hypotenuse) = a/[a*sqrt(2)] = 1/sqrt(2)
gasper said:
sketch an isosceles right triangle. the two equal acute angles are both 45 degrees = pi/4 radians. if the two equal sides have length "a", the hypotenuse has length "a*sqrt(2)".
cos(pi/4) = (adjacent side)/(hypotenuse) = a/[a*sqrt(2)] = 1/sqrt(2)