Question 516242
how do you solve this:
sin(11π/8) =
sin(π/8)=
**
sin(11π/8)=(22π/8)/2=(11π/4)/2
sin half angle formula: sin s/2=±√[(1-cos s)/2]
sin (11&#960;/4)/2=±&#8730;[1-cos(11&#960;/4)/2] (select negative root because sin(11&#960;/8) is in quadrant III where sin<0)
cos(11&#960;/4)=-&#8730;2/2 in quadrant II where cos<0
&#8730;[1-cos(11&#960;/4)/2]=&#8730;[(1-(-&#8730;2/2))/2]=&#8730;[(1+&#8730;2/2)/2]=&#8730;(2+&#8730;2)/2
sin(11&#960;/8) =-&#8730;(2+&#8730;2)/2
..
sin(&#960;/8)=(2&#960;/8)/2=(&#960;/4)/2
sin (&#960;/4)/2=±&#8730;[1-cos(&#960;/4)/2] (select positive root because sin(&#960;/8) is in quadrant I where sin>0)
cos(&#960;/4)=&#8730;2/2 in quadrant I where cos>0
&#8730;[1-cos(&#960;/4)/2]=&#8730;[(1-&#8730;2/2)/2]=&#8730;(2-&#8730;2)/2