Question

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If:

sin(3pi / 10) = (1 + squareroot 5) / 4

Find the exact value of cos(pi / 5)

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Thankyou very much. Of course, all help is appreciated.

Answer 1

this might be easier to handle if you think in degrees.
pi/5 radians = 36º and
3pi/10 rad = 54º

did you notice that they add up to 90º and did you know that the cos (any angle) = sin (90 -any angle) ?

so cos(36º)= sin(54º) = (1+√5)/4

BTW, cos 36º is exactly half the Golden Ratio, which would bring me to the Fibonacci numbers and other most fascination topics that I could spend hours ......