How can we find out the value of sin18° ???

(without using calculator)

Question

How can we find out the value of sin18°  ???

(without using calculator)

mayankdevnani · Answer

anyone???? please don't shy, answer it....

dumbcow · Answer

i know the exact answer but not sure how to come up with it....i dont see any combination of half angles , sum/difference angles to get 18
it may be done with a minimal polynomial maybe

mayankdevnani · Answer

so can you help me???

anonymous · Answer

we need to use0°, 30°, 45°, 90° etc
example, 
18°=x.

we can use 90°, right? 
90°= 5.18°
mean 5x.

sin 5x= sin 90°
sin(x+4x)=1

continue it.

dumbcow · Answer

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/simpleTrig.html its the golden ratio!!

mayankdevnani · Answer

i can't understand.  @Machida

anonymous · Answer

letx=18*
5x=90*
3x=90*-2x
cos3x=cos(90*-2x)=sin2x
4cos^3x-3cosx=2sinxcosx
since cosx is not=0
4cos^2x-3=2sinx
4(1-sin^2x)-3=2sinx
4sin^2x+2sinx-1=0
sinx=[-2+/-rt(2^2-4*4(-1))]/2*4
sin18*=(-1+/-rt5)/4
18* is an acuteangle.so sin18*>0
therefore sinx=(-1+rt5)/4

hope u understand !!!!