Find the exact value of cos pi/16

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Find the exact value of `cospi/16` .

We use a half-angle formula: `cos (alpha/2)=sqrt(1/2(1+cos alpha))`

(1) `cos pi/8=cos(pi/4)/2=sqrt(1/2(1+cos pi/4))`




(2) `cos pi/16 = cos (pi/8)/2`

`=sqrt(1/2(1+cos pi/8))`




Thus `cos pi/16 = (sqrt(2+sqrt(2+sqrt(2))))/2~~.9807852804`

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