Question 738265
What is the exact value of sine of 13pie/12 ?
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{{{sin(13pi/12)=sin(pi+pi/12)=-sin(pi/12)}}} (in Q3 where sin <0)
Use sin half-angle formula to solve: {{{sin(s/2)=sqrt((1-cos(s))/2))}}}
sin(&#960;/12)=sin((&#960;/6)/2)
=±&#8730;(1-cos(&#960;/6)/2)
=-&#8730;(1-(&#8730;3/2)/2)
=-&#8730;(2-&#8730;3/4)
=-&#8730;(2-&#8730;3)/2
Check with calculator:
sin(13&#960;/12)&#8776;-0.2588..
-&#8730;(2-&#8730;3)/2&#8776;-0.2588..