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lcrpn

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10 years, 248 days
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then how to calc "sin(pi/16)"...

lcrpn 20
January 20 2014
0 0

@Preben Alsholm 


Then how to calc sin(pi/16)?, we know it should be "1/sqrt(1+(1+sqrt(2)+sqrt(4+2*sqrt(2)))^2)".


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``

``

> 

identify(evalf(sin((1/16)*Pi)))

.1950903221

 (1)
> 

evalf(sin((1/16)*Pi)-1/sqrt(1+(1+sqrt(2)+sqrt(4+2*sqrt(2)))^2))

0.1e-9

 (2)
> 

``

``


Download sine.mw

"Tried many, only this works properly:"...

lcrpn 20
January 20 2014
0 0

@Markiyan Hirnyk 

> 

f := proc (x) options operator, arrow; sin(x)+cos(x+(1/5)*Pi) end proc

proc (x) options operator, arrow; sin(x)+cos(x+(1/5)*Pi) end proc

 (1)
> 

simplify(convert(collect(convert(expand(f(x)), sincos, {cos(x), sin(x)}), {cos(x), sin(x)}), phaseamp, x))

(2-2*sin((1/5)*Pi))^(1/2)*cos(x+arctan((sin((1/5)*Pi)-1)/cos((1/5)*Pi)))

 (2)
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